You've put the table loop on the outside, which is good. If it was on the inside, you'd be compiling a lot of regexps for nothing. But it can be taken a step further.

my $tableList = map qr/$_/i,
                join '|',
                map quotemeta,
                @tableList;

for my $Q (@fileList) {
   push @tableUsed, $Q =~ /$tableList/g;
}
[download]

The OP might want to remove duplicates from @tableUsed.

my $tableList = map qr/$_/i,
                join '|',
                map quotemeta,
                @tableList;

my %tableUsed;
for my $Q (@fileList) {
   for my $W ($Q =~ /$tableList/g) {
      ++$tableUsed{$W};
   }
}

my @tableUsed = sort keys %tableUsed;
[download]