Search::QueryParser supports quoted constructs :) But if you want your regex see Regexp::Grammars::Common::String or Regexp::Common

use YAPE::Regex::Explain;
print YAPE::Regex::Explain->new(
qr/(?:(?:\")(?:[^\\\"]*(?:\\.[^\\\"]*)*)(?:\")|(?:\')(?:[^\\\']*(?:\\.
+[^\\\']*)*)(?:\')|(?:\`)(?:[^\\\`]*(?:\\.[^\\\`]*)*)(?:\`))/
)->explain;
__END__

The regular expression:

(?-imsx:(?:(?:\")(?:[^\\\"]*(?:\\.[^\\\"]*)*)(?:\")|(?:\')(?:[^\\\']*(
+?:\\.[^\\\']*)*)(?:\')|(?:\`)(?:[^\\\`]*(?:\\.[^\\\`]*)*)(?:\`)))

matches as follows:
  
NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  (?:                      group, but do not capture:
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      \"                       '"'
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      [^\\\"]*                 any character except: '\\', '\"' (0 or
                               more times (matching the most amount
                               possible))
----------------------------------------------------------------------
      (?:                      group, but do not capture (0 or more
                               times (matching the most amount
                               possible)):
----------------------------------------------------------------------
        \\                       '\'
----------------------------------------------------------------------
        .                        any character except \n
----------------------------------------------------------------------
        [^\\\"]*                 any character except: '\\', '\"' (0
                                 or more times (matching the most
                                 amount possible))
----------------------------------------------------------------------
      )*                       end of grouping
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      \"                       '"'
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
   |                        OR
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      \'                       '''
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      [^\\\']*                 any character except: '\\', '\'' (0 or
                               more times (matching the most amount
                               possible))
----------------------------------------------------------------------
      (?:                      group, but do not capture (0 or more
                               times (matching the most amount
                               possible)):
----------------------------------------------------------------------
        \\                       '\'
----------------------------------------------------------------------
        .                        any character except \n
----------------------------------------------------------------------
        [^\\\']*                 any character except: '\\', '\'' (0
                                 or more times (matching the most
                                 amount possible))
----------------------------------------------------------------------
      )*                       end of grouping
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      \'                       '''
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
   |                        OR
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      \`                       '`'
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      [^\\\`]*                 any character except: '\\', '\`' (0 or
                               more times (matching the most amount
                               possible))
----------------------------------------------------------------------
      (?:                      group, but do not capture (0 or more
                               times (matching the most amount
                               possible)):
----------------------------------------------------------------------
        \\                       '\'
----------------------------------------------------------------------
        .                        any character except \n
----------------------------------------------------------------------
        [^\\\`]*                 any character except: '\\', '\`' (0
                                 or more times (matching the most
                                 amount possible))
----------------------------------------------------------------------
      )*                       end of grouping
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      \`                       '`'
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
  )                        end of grouping
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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