For this if I scan line-by-line in a perl program then it will just slightly better than a C program.

You´re wrong. To scan the whole file you will have to slurp it into memory first. That´s bad, especially when the target for myExp is likely to be near the beginning of the file.
However, here is how to read a file at once and apply a regex to the content:

use strict;

my $data;

slurpfile ("yourfile.txt", $data);

print $1 if $data =~ /(expression)/m;

sub slurpfile
{
    
  local $/ = undef;
  
  open IN, "<", $_[0] or return 0;
  $_[1] = <IN>;
  close IN;

  return 1;
}
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