Speaking to the media ahead of Man City's Community Shield meeting against Manchester United on Saturday, Guardiola praised Alvarez's contribution while admitting he learned a lot from the forward.
"First of all I want to say my gratitude for Julian, we won everything, his contribution has been massive," the City boss said. "He was incredibly loved by the team for his behaviour but if he wants to leave, a new challenge - Atletico is a top club - then if you want to leave it's OK. We wish him the best. I learned a lot from him, hopefully he can find what he was looking for."
Guardiola continued by saying Alvarez had told him that he was seeking a new challenge.
"I don't know the reason why, he said to me he wants a new challenge, he feels it's what he needs to do," he added. "Last season he played a lot, at some moments with Erling, but I understand in certain moments he didn't play. I said to the club many times at the end the club has the end decision but I say that contracts can be broken, if you are not happy why should you be here? He believes his period here must be over so OK, both clubs arrived at an agreement and that's all."