You Could use a custom sort routine:

use warnings;
use strict;

my @arr = ('TEXT1','TEXT11','TEXT13','TEXT2','TEXT3');
print "BEFORE:\n";
print "\'$_\'\n" for @arr;

## pass code block to sort to control sort behaviour
@arr = sort by_numbers @arr;

## look again
print "AFTER:\n";
print "\'$_\'\n" for @arr;

sub by_numbers{
    my $a_num = $a =~ /^TEXT(\d+)$/;
    my $b_num = $b =~ /^TEXT(\d+)$/;

    ## maybe also include checking that $a_num and $b_num are defined

    return ($a_num <=> $b_num);
}
[download]

Updated: Typo in code