Nicolas Hofler struck in the 86th minute to end Pep Guardiola's 100 per cent record in the league so far this season, with Bayern opting to rest several players ahead of Friday's European Super Cup clash with Chelsea.
Lahm, however, insists his side have no excuse for failing to see out the win on Tuesday.
"We have only ourselves to blame," the Germany international was quoted as saying on the club's official website.
"We conceded an equaliser just before the end, but we had plenty of chances to score a second of our own before that. It would have been over if we’d done that.
"In recent matches, we’ve tended to fail to make the outcome clear-cut, and we were punished for that today."
Bayern sit atop of the Bundesliga table with 10 points from four games, holding a one-point lead over Borussia Dortmund, Bayer Leverkusen and Mainz, who all have a game in hand.
