Look at this code and check for differences. Your -f test was being regexed, not the filename. Also you filled your array improperly.

#!/usr/bin/perl
use warnings;
use strict;
use File::Find;

find(\&file_names, '.');

my @files;
print "@files\n";

sub file_names {

  # if( -f && $File::Find::name=~/(.*).txt$/)  #bad usage of .*
 
  if( -f && $File::Find::name=~/\.txt$/)  # thanks davido :-)
   {
       print "$File::Find::name\n";
       push @files, $File::Find::name;
     }
 }
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