Cristiano Ronaldo and Sergio Ramos struck braces in Real's 4-0 second-leg thrashing of the Bundesliga champions at the Allianz Arena, completing a 5-0 aggregate victory.
And Guardiola admitted it was his error that led to Bayern's humiliating defeat, but insisted it's impossible for the team to win every title.
"We played badly when we had the ball. That's my responsibility. I made a mistake," the Spaniard told reporters.
"I was wrong on some tactical issues. It’s my responsibility. When you don’t play well, these things happen against great rivals, but I’m disappointed.
"This team has to win everything so that people are happy. Sometime it’s not possible. I’m sorry for the disappointment of not playing well.
"Three years ago Bayern won zero titles in a season. If you win the league it may be enough but we knew that this year could only equal the past. We won’t but that’s the sport.
"Today there has been a team that has been better. I still have the impression we’ve had a good Champions League campaign but Real Madrid had the quality and the first-half won it for them."
"It’s difficult for me and my players. I’m still proud of them.
"The reason for the defeat isn’t related to the possession. Football is played with the ball and then there are other things.
"It was a bit better in the first-leg, but congratulations to Real Madrid."
Guardiola lamented his side's defending from set-pieces, with Ramos heading in a corner and free-kick in the first half.
Ronaldo netted on the counter-attack before half-time and completed the scoring with a cheeky free-kick which went under a jumping Bayern defensive wall.
"We have to carry on now. If you don't play well and you defend set-pieces badly, that's just how it is. You are being punished," Guardiola said.
"We are at the highest level in Europe; such mistakes are punished right away."
Guardiola said he had been hopeful Bayern could reproduce the performances they put in against Premier League sides Arsenal and Manchester United earlier in the knockout stages.
"What we did against Arsenal and Manchester [United] did not work today," he said.
"Also in the first-leg in Madrid we had more control than today and at least a couple of chances. Today, just a few. That's why we have lost the semi-final.
"You play with the ball and if you don't have it that doesn't work."