Villa believes anything is possible for the Catalan club.
"We can fight for the treble," he said. "We are playing for three titles at the moment, and we are going to try to go step by step, with humility, to try to win all three.
"It will take a lot of hard work, but we are still alive in all three competitions and we are going to fight until the end in all three - we can only promise that."
Villa's goal against Athletic means he has scored in the last three games - his best run so far as a Barca player.
"I'm happy with my form and the numbers, although I'm more concerned with how people have reacted to me," he said. "That tells me I'm doing well."
The 29-year-old is also delighted at Guardiola's contract renewal, even if it is initially only for one more year.
"It's great news for the club," he said.
"He prefers to sign yearly contracts and that's what works for him, but I would love to play for Guardiola for the rest of my career."