Is there a reason why you want to do this with a regex? It isn't really the right tool for the job.

I would probably just use grep to get a list of the missing items.

my @words   = qw( foo bar );
while (my $line = <DATA>) {
    chomp $line;
    my @missing = grep {$line !~ $_} @words;
    printf "line: %-10s; missing: %s\n", $line, join ',', @missing;
}
__DATA__

foo
bar
foo bar
[download]

Or use List::Util's first, which will abort the search once one is missing.

use List::Util qw( first );
my @words   = qw( foo bar );
while (my $line = <DATA>) {
    chomp $line;
    my $missing = first {$line !~ $_} @words;

    printf "line: %-10s; missing: %s\n", $line, $missing;
}
__DATA__

foo
bar
foo bar
[download]

Note that this will only return the first missing item, and if you're searching for something like "0" then you should check whether $has_missing is defined.