The easiest solution: wrap your regular expression in a while loop:

#!/usr/bin/perl
use strict;
use warnings;

$_ = 'aadsdfaasfga';

my $count;
$count++ while /a/g;

print "$count\n";
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For a shorter and more clever solution, cast the match into list context and then count the matches:

#!/usr/bin/perl
use strict;
use warnings;

$_ = 'aadsdfaasfga';

my $count =()= /a/g;

print "$count\n";
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Finally, to literally accomplish your goal, you can embed Perl code in the regex (see A bit of magic: executing Perl code in a regular expression). There are on-point examples in the link, but I'd recommend against it.