As a dog owner you must understand your dog behavior. Like us humans, dog may act different if scared and if the things around him are new. Dog first visit to a vet may cause him to act differently-its normal.
You may notice that your dog is stressed and quivered. If this happened, try to relax and calm your dog by cuddling him. This will help him feel secured.
The veterinarian may give him a couple of shot and this may be the reason for him to feel lethargic. It is normal just let him rest and he will be alright again. I remember my dog still a puppy back then for his first vet visit for vaccine shots. He got wary after the two shot and rest in my lap but as soon as we got home he is good as new. This may feel you a little upset as I feel when I saw may dog get listless but dog need vaccines. Just make sure to give comfort for your dog especially treats to help him feel alright.