It depends what purpose you're using this for. If it's something like a password manager where you're checking the user's existing passwords to see if any have been breached, then yes, you should make sure not to hit false positives.

But if you're using it as a way to prevent people from using known-breached passwords on a site/service, it's really not worth worrying about. False positives would only be a problem when the user is using bad password practices anyway. If it's a non-shared, random password like it should be, a tiny chance of blocking an acceptable one is fine. They can just generate another one, it's an extremely minor inconvenience at worst.

Just include a note in the error message saying something like, "In very rare cases, this could be a false positive. Even if it is, you must choose a different password." The 0.1% of users it impacts (or whatever your error rate is) will be fine.