The reigning European champions enjoyed the lion's share of possession in the semi-final first-leg encounter at the Bernabeu, yet were unable to take a goal back to Germany as Karim Benzema's lone strike settled the match.
Bayern captain Lahm paid tribute to Real's counter-attacking capabilities, but felt that his team were let down by poor fortune and expects them to put up a fight on home turf in next week's second leg.
"We lacked the little bit of luck you need and the killer attacking moves," he told the club's official website. "You could see we were determined to win for the full 90 minutes.
"We knew Real would play defensively and use their superb counter-attacking players. We tried to stop them hitting us on the break. We succeeded at times, and at other times we didn't.
"We were obviously hoping for a different result, but we have every chance of winning by two clear goals at home.
"I'll go back to Munich feeling positive. Anything is possible at the Allianz Arena. We've often shown we're capable of turning matches around."
Despite the defeat, head coach Pep Guardiola paid tribute to his side's "courageous" efforts in Spain.
"The only thing I asked of the players is to be true players and come to the Bernabeu to steal the ball and play, play and play," he said.
"We missed some chances of scoring a goal and I think being in the last four we made enough chances to score at least one goal.
"We didn't create just one, or two, or three or four or five, we created even more than that. I asked to my team to be courageous (and) to defend Bayern’s name and to let Europe see a team who is courageous and is willing to win a game as we did and as I have tried to do as a coach during my career."
