Bayern goalkeeper Manuel Neuer gifted Gladbach the lead 11 minutes in when he gave Marco Reus an empty net to fire into by passing the ball straight to the Germany international.
Patrick Herrmann doubled the home side's advantage just before the interval and then struck again in the second half to render Bastian Schweinsteiger's late goal for Bayern purely academic.
Lahm argued afterwards that the visitors only had themselves to blame for their loss and that while Monchengladbach are now just a point behind them at the top of the table, he is more concerned with the threat posed by third-placed Dortmund, who are three points behind with a trip to Hamburg to come on Sunday.
"We made too many mistakes and conceded unnecessary goals," Lahm told Bayern's official website. "And for this, you will be punished.
"In the second half we tried everything, but again ran into a purely counterattacking game.
"You can prepare well but there is always the danger of being caught out in the first game back [after the winter break].
"We were unable to maintain our momentum. Our biggest enemy - besides ourselves - is still [third-placed Borussia] Dortmund."
Meanwhile, Bayern coach Jupp Heynckes took a pop at the perceived negative nature of Monchengladbach's tactics.
"The key point in the game was Borussia's goal just before the break, which made it 2-0," he reasoned.
"Then it is difficult to come back against a team that defends so well, which is very well organised defensively and puts ten players in their own penalty area," he concluded.
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