It was an astonishingly inept display from a side which had been the dominant force in Europe over the past 18 months.
Ronaldo added his second at the death to book Madrid's place in the final.
"We're very disappointed because we set our sights high, but suddenly we were 2-0 down after 20 minutes from two set-pieces," Lahm said on the Bayern website.
"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."
Arjen Robben said Madrid were the "world's best counter-attacking team", but added: "A 4-0 defeat at home is a choker."
Bayern chief executive Karl-Heinz Rummenigge admitted the loss exposed the limitations of the Bundesliga champions. They failed to find the net against Carlo Ancelotti's side in 180 minutes of football.
Rummenigge said: "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.
"We need to lick our wounds quickly, because we want a much better performance on May 17 in the DFB-Pokal final against (Borussia) Dortmund."
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