After the first leg finished 1-1 at Old Trafford, the tie swung in United’s favour when Patrice Evra slammed home a stunning 25-yard drive after 57 minutes to put the visitors in front at the Allianz Arena.
Rather than wilt, however, Bayern equalised immediately through Mario Mandzukic before quickfire goals from Muller and Arjen Robben saw Bayern through 4-2 on aggregate.
At 1-0 down, Germany international Muller admitted: “It did not feel good. Evra had a shot which was simply unstoppable. But our mentality is very good and we have superb leaders that march forwards and we wanted to equalise so badly. We reacted well.
“In the end the goals were the decisive factor in the tie. We ran a lot to score our goals and to get the 1-1 so quickly after we conceded. Then we were able to score another two and could be a little bit more relaxed.”
Bayern made no secret of their dislike for United’s defensive tactics after the Old Trafford encounter but Muller felt Mandzukic, who started that game on the bench, made a difference back in Bavaria.
He added on Sky: “It was a bit annoying after the first leg. We had some situations that reminded us of handball. We did not manage to create clear chances. There were some good situations, but no 100% chances. You start to wonder what to do.
“Today, with me and Mandzu in the box we were a little more dangerous and it helped that one of us took one defender off the other one. In the end our tactics worked.“
Bayern boss Pep Guardiola was delighted his side had remained patient before finally breaking United down.
"I knew it would be tough. This is the Champions League quarter-final and Manchester had their keeper plus eight players in the box,” he said.
“But we were patient and we had a little luck in converting our chances. Now we have reached the semi-final and I am very, very proud of my team."