After Isco bagged a first-half brace and Chelsea's Alvaro Morata sealed the victory in the 77th minute, Villa was subbed on by manager Julen Lopetegui to make his 98th national appearance -- over three years after his last cap.
"I've always said it was difficult for me to come back, but I had not given up the dream. It makes me very happy to be here," Villa said after the match.
"To all those who have trusted me to come, thank you. It was a key moment with this game for qualification.
"The feeling is very difficult to describe, I'm very happy. Thanks to everyone. I do not know if I deserve so much love."
Asked if he thought he could make two more appearances to reach 100 caps, Villa said: "You have to go step by step. Now it is time to rest, try to play the 99th and then we will see."
Villa also paid tribute to match-winner Isco, whose two goals moved Spain three points clear of the Italians at the top of Group G.
"I know Isco from the Valencia youth set-up, he was already training with the first team and knocking on the door," Villa said.
"He is a great guy and he is in a great moment. I'm very happy for him. We can all enjoy him because he is Spanish, thank God. We will enjoy him for the national team."
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