This will uc the first letter following < and </:

$string =~ s!(</?)([^/>])!$1.uc($2)!eg;
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The key is the /e modifier on the regexp, which indicates that the right-hand side of the substitution regexp is Perl code which needs to be evaluated, rather than just a plain string.

Breaking it down into its components:

s!
  (</?)      # Match and capture '<' followed by optional '/'
  ([^/>])    # Match and capture the next char, as long as
             # it's not a '>' or '/'.
 !
  $1         # Replace with '<' or '</'.
  . uc($2)   # Concatenate with the uc of $2.
!egx
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This approach is error-prone though. What if the literal text (not found inside a tag) has a '<' character int it? You don't have to write your own parser, when CPAN has many already written.