Calling Regex Experts

[D . J .]

OK, I'm stumped.  I need to create a regex that will match if anything other than two terms I've specified exist.

So for example, I have two terms I like, say "cat" and "dog".  I want the rule to match if a string contains anything other than cat or dog.

I tried ...

$value !~ /cat|dog/

...but this had the unintended consequence of still matching a string like "cat dog bird" or "cat bird" since the string does contain one of my two terms.  So what do I need to do?  Thanks in advance!

- D.J.