Keep your enemies closer
If you're torn between letting his foul become water under the bridge and tearing his face off, sometimes the best policy is feign forgiveness, but never forget. In other words, keep your enemies close.
By letting him believe he's still in your good graces (even if he's totally not), he'll act with more respect going forward, rather than talking smack behind your back and otherwise continuing the unneeded drama. At worst, he makes the same mistake again and confirms your lingering doubts about his character. At best, he works harder to be a better, more trustworthy friend. Either way, it works in your favor.