The reigning champions only lost 1-0 in the Bernabeu but were annihilated in front of stunned home fans at the Allianz Arena as Real raced into a 3-0 first-half lead.
Cristiano Ronaldo grabbed his second of the night in the dying stages to add further emphasis to the scoreline - but Lahm was adamant the sloppy defending that allowed Sergio Ramos to score twice in the first 20 minutes was to blame.
The Germany full-back told the Bayern website: "We're very disappointed because we set our sights high, but suddenly we were 2-0 down after 20 minutes from two set-pieces.
"That really leaves a bitter taste. I don't think we played well tactically in the first half. The game was too open.
"It was the opposite of the first leg when we controlled the play. I know they hit us on the break last week, but (on Tuesday) it was end-to-end stuff in the first half.
"That's fundamentally not the way we play our football, but it's what Real really like. It totally played into their hands."
Bayern chief executive Karl-Heinz Rummenigge was equally disappointed, adding: "We didn't have quite enough passion to cause our opponents serious problems.
"We were obviously unlucky to go two goals behind to set-plays. After that it was obvious Real would make the final.
"Real have a magnificent team at the moment and our limitations have been exposed to a certain extent.
"You get games like these, but we need to hold our nerve. We've been a little spoiled because we made the final twice in a row, and three times in the last four years.
"Despite the anger you feel welling up inside, I think on days like these you have to stay calm, go home and try to do things better as of tomorrow."