The Barcelona forward scored his side's fourth goal from the penalty spot in their 5-0 win in what was his first game for La Furia Roja in nine months.
"I am happy to be here again," Villa told TVE. "I have had a hard time out there.
"I have missed my national team so much, the games and the [training camps] with my teammates. But I will not look back."
Villa missed Spain's successful Euro 2012 campaign because of injury.