The Citizens have won everything under Guardiola, except Europe's premier cup competition.
But Villa, who worked under Guardiola at Barcelona, says City's 'obsession' with the trophy will eventually pay off.
"For all the coaches and all the big clubs, it's normal to focus on the Champions League, because it's the best tournament you can play with a club," he told The Mirror.
"Pep is obviously one of the best coaches in the world and obviously the subject of his focus is to win all the trophies.
"Manchester City have never won this trophy, they've been behind in terms of it for many years, so it's normal they have a big obsession with this kind of trophy.
"It's the best tournament you can play as a soccer player, but it's difficult to win for everyone, not just one or two clubs.
"It's very difficult to win, and obviously you need to do a lot of work to win it."
Villa added: "He's a great coach," Villa said. "I was with him for two fantastic years at Barcelona and he helped me a lot.
"He will have success wherever he goes. He managed in Spain and was successful, the same in Germany, and now in England.
"So wherever he manages, he will be successful, because he's such an amazing coach."