This is only my opinion; I am not a qualified lawyer. If you chose to take the matter further you will need to seek qualified legal advice and frankly due to the relatively small sums involved that may not be practical. That being said:

Theoretically you could claim for the tort of negligence and if successful recover damages (your vet’s bills).

If your dog is insured and you make a claim under your policy the insurance company may pursue the above claim but as previously mentioned this is unlikely due to the relatively small amounts of money involved.

To be honest legal remedies are hardly ever practical in situations were only relatively small amounts of money are involved.