Peruvian forward Claudio Pizarro went down rather easily under a challenge from defender Michal Zewlakow and Dutch striker Roy Makaay converted from the spot to win the game for the Bavarians and send them through to the last 16 of the UEFA Champions League.
"It was a clear foul in the box," Hitzfeld said at a news conference. "Makaay took the chance with icy coolness."
The Bundesliga side dominated for most of the game, although Oliver Kahn had to pull off a world class save at the death to deny Oleg Iachtchouk.
"We have Ollie Kahn to thank yet again after he made that spectacular last-minute save," said Hitzfeld.
"I aged a few years tonight," he added. "We let our opponents gain confidence and our own nerves were exposed more and more."
Anderlecht coach Hugo Broos said his players were convinced Bayern's first-half penalty had been awarded unfairly.
"Belgium is a small country, perhaps that's the reason," he told reporters.
"We dominated the Bavarians at times and if any team deserved to win then it was us," he added. "We really have deserved better given the effort we have put in."
