The 24-year-old moved to Real Madrid this month after talks with Bayern over a new deal at the Allianz Arena had stalled earlier this year.
Guardiola admits the Bundesliga champions did their utmost to convince the World Cup winner to stay but has wished him well in his new career in Spain.
"We tried to convince him to stay at the club but I understand. He is young and wants new challenges. It is his decision and we have to respect that," he told a press conference.
"I hope he is happy in Madrid. It was an honour to be his coach. I wish the very best to him and his family. At the same time I want to say thank you for what he did last season."
Guardiola went on to call for patience from supporters concerning new striker Robert Lewandowski, despite the Poland international scoring on his debut in pre-season.
"Maybe he will need some time but he has the quality, he did everything to come to this club," added the former Barcelona boss.
"I am here to support him. He will have the opportunity to have a good life with his family over here in Munich. The rest will come by itself but we will need time - a change like this is never easy.
"He will get the time that he needs here."
Guardiola guided his side to the domestic double in his first season in charge of Bayern, while a number of his first-team stars went on to lift the World Cup with Germany in Brazil this summer.
Bayern CEO Karl-Heinz Rummenigge claimed Guardiola would have few problems motivating the squad to achieve even greater success in 2014-15, but the 43-year-old has conceded it could be a tough task.
"If you have won some titles, you become a little bit more loose and relaxed," he added.
"That is the challenge for a coach - and it is a big challenge. We have to maintain the level of last year with this team.
"That is going to be quite difficult as a lot of important players were at the World Cup. It is a huge challenge, but I want to take it."