The Bundesliga leaders withdrew their offer of a new contract after Germany full-back Lahm failed to respond before a deadline set for midday on Tuesday.
On Thursday, Beckenbauer claimed Lahm, who is represented by the same agent as Owen Hargreaves, had set his sights too high.
"Lahm's demands were a little too high in the eyes of our board (of directors)," he explained.
"Of course you can make demands and hope to get something, but whether you do get it is another question."
It now looks increasingly likely that Lahm will leave the club, whether it be for a fee this summer or on a free transfer when his current deal expires 12 months later.
"It does not have to be that he leaves us now - his contract still runs until 2009," Beckenbauer told Premiere television.
"I don't think the last word has been spoken yet, though.
"He fits in well here and has proven that he is a world-class player and it would be great if he stays. But, on the other hand, you cannot change a player's mind when he has a huge offer and decides to move abroad."