Bayern twice recovered from behind with goals from Franck Ribery and Javi Martinez, the latter the final kick of 120 minutes of enthralling action, to triumph 5-4 on penalties.
While Mourinho hinted at a conspiracy and was bitter in defeat following the dismissal of Ramires for two yellow cards, Guardiola lauded the ability of the team he inherited from Jupp Heynckes.
The Spaniard, back in football after a year-long sabbatical following four years of success at Barcelona, dedicated the shootout success to his predecessor, who won the European Cup in May as part of a treble-winning campaign.
"It was an incredible final," Guardiola said.
"We won and we are happy. The personality of our players is incredible.
"I have really noticed now why they won everything last season, given the strong character and personality that they have. I'm very happy for them."
Bayern's efforts were typified by Ribery, the newly-crowned European Player of the Year.
The France forward scored a wonderful solo goal early in the second half, having gone close on numerous occasions in the first period.
Ribery was Bayern's go-to man and was a deserved man of the match.
"I'm very happy indeed, I'm elated after Friday's award in Monte Carlo, I was really over the moon," Ribery said.
"We played 120 minutes and we had a penalty shootout, but I'm so happy for the entire team and the coach.
"It was a very special occasion for him. His rivalry with Mourinho is legendary, but we had a lucky outcome on our side."
Ribery was pleased Bayern could secure a first trophy of Guardiola's reign.
"Yes, I think it's important for him," Ribery added.
"Of course we won everything, the treble, last year. It's not easy for Pep to follow in these footsteps and of course the whole team feels pressure, but more so even the coach.
"This helps us, this gives us the necessary impetus, but he's an excellent coach.
"He does excellent work and we're very satisfied with him."