The reigning European champion headed into the second leg at the Allianz Arena with only a slender 1-0 deficit but two Sergio Ramos goals and a Cristiano Ronaldo strike quickly put Carlo Ancelotti's men firmly on the front foot.
A late Ronaldo free kick added insult to injury and sealed a 4-0 win on the night, and the Bundesliga champions' captain was highly critical of how the team played out the clash in comparison to the relatively even opening leg at Santiago Bernabeu.
"The disappointment is huge," Lahm told reporters after the defeat. "We wanted it a lot but then we were 2-0 down after 20 minutes thanks to two set pieces. This is incredibly bitter and disappointing. We believe it's better to go for zonal marking at set pieces. We went down early again, then it was 2-0. We did not play well tactically, we had an open game way too early.
"While we controlled the first leg, we gave them an end-to-end game today, that's not our way of playing. They like it though."
Madrid will now face city rival Atletico Madrid or Chelsea in next month's final.