I am sorry for your loss.
No, you are not obligated to pay credit card debts that were in his name only.
However, his estate is responsible for the payment of those debts. You did not indicate if he left an estate or if the estate is being probated.
If the estate is being probated, the creditors will submit their claims to the court.
If he left no estate, simply write a letter to the creditor, attach a copy of the death certificate and tell them there is no estate.