Similar to the solution from pc88mxer, this keeps the regexs and the counts together.

use List::Util qw( first );

my @re_count = map { { re => $_, count => 0 } }
               ( qr/this/, qr/that/, ..., qr// );
foreach my $row ( ... ) {
    my $re_ref = first { $row =~ $_->{re} } @re_count;
    $re_ref->{count}++ if $re_ref;
}
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The map turns each regex into a hash reference containing the regex and a counter. Then, for each row, we loop over those with first from List::Util to get the first one with a regex that matches. If there's a match, increment its counter.

I like this kind of data structure (AoH) because I can pile more data into the hash refs later if I want to. For example, I could add a human readable name to each item for reporting.