perlre can:

\Z Match only at end of string, or before newline at the end
\z Match only at end of string

Update Consider:

my $str = "The quick abc";

for my $regex ('\babc\z', '\babc\Z') {
    print "Matched with newline using $regex\n" if "$str\n" =~ $regex;
    print "Matched without newline using $regex\n" if $str =~ $regex;
}
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Prints:

Matched without newline using \babc\z
Matched with newline using \babc\Z
Matched without newline using \babc\Z
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Thanks for your replay.
Its clarifies me.

use strict;
use warnings;
use YAPE::Regex::Explain;

for my $regexp ('\babc\z','\babc\Z') {
    print YAPE::Regex::Explain->new($regexp)->explain, "\n"x3;
}
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The regular expression:

(?-imsx:\babc\z)

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):
----------------------------------------------------------------------
  \b                       the boundary between a word char (\w) and
                           something that is not a word char
----------------------------------------------------------------------
  abc                      'abc'
----------------------------------------------------------------------
  \z                       the end of the string
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------



The regular expression:

(?-imsx:\babc\Z)

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):
----------------------------------------------------------------------
  \b                       the boundary between a word char (\w) and
                           something that is not a word char
----------------------------------------------------------------------
  abc                      'abc'
----------------------------------------------------------------------
  \Z                       before an optional \n, and the end of the
                           string
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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