This is pretty common after vaccines. Keep an eye on his breathing. If it is troubled, you may want to give your vet a call as this could be an allergic reaction.
Many vaccines are given intramuscularly so they can cause some pain and fatigue, must like when a human baby gets vaccines.
If you don't start to see some improvement within the next 24 hours, you will want to see your vet.
Let me know if you still have questions.