...
my @handles = map { open my $fh, '<', $_; $fh } @files;

for my $index (0 .. $#files) {
    next unless $handles[$index]->opened();

    while (<$handles[$index]>) {
        if (/a particular pattern/) {
            print "Pattern found in $files[$index]\n";
            last;
        }
    }
}

close $_ for grep { $_->opened() } @handles;
...