Unrelated tips:

• I hope you're using use strict; use warnings; or equivalent, but simply left it out for brevity.
• It's good that you included the file name in the error message, but it would be nicer if you included the error cause ($!) too.
• next if $row eq ""; and chomp $row; don't actually achieve anything here.
• my $qfn = $ARGV[0]; would be less weird than foreach ($ARGV[0]). But why not go for the flexibility of for my $qfn ( @ARGV )? At which point, the loop and the file handling stuff can be replaced with while ( <> ).
• Adding use v5.10; or higher would allow you to use the nicer say $1; instead of print "$1\n";.
• You could use $& instead of $1 and the capturing parens. (This makes no difference.)

use v5.10;
use strict;
use warnings;

my $re = ...;

while ( <> ) {
   say $1 while /$re/g;
}
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