By ESPNSTAR.com staff
Frankfurt, newly promoted to the German top-tier, have exceeded all pre-season expectations and were just seven points behind Bayern prior to the game.
And they showed they were no pushovers, proving to be extremely difficult to break down for the league leaders.
However, Javi Martinez managed to break the offside trap and pass to an unmarked Franck Ribery for the first goal towards the end of the first half while David Alaba confirmed the victory after netting a second-half penalty.
But Heynckes was not averse to giving credit to the losing side, known as the Eagles, as he told the club website, "It was a hard-fought victory against a very good team.
"We didn't look determined enough, particularly in the first half, and Frankfurt played good football and were full of running.
"It's hard to re-focus after the Champions League. You can't always score six goals and play superb football. But we showed that we're capable of the right reaction in a difficult situation.
"In that sense, the team were excellent. We made the most of our experience and intelligence."
Bayern defeated Lille with an emphatic 6-1 scoreline in the Champions League during the week but the 67-year-old feels that the club's packed fixture list will make it difficult to grind out wins on a continual basis.
"Playing three days doesn't make things easy, and that was the case today [Saturday]," he said.
"Frankfurt were fresher. But we had lots of chances and should have taken the lead earlier.
"Winning today was important because we're on international duty now."
Frankfurt coach Armin Veh admitted that Bayern were just too good for his plucky young side.
"Unfortunately, we were not rewarded for our performance, but we were playing against opponents who are in a league of their own," said Veh.
"We tried to press Bayern early and not let them get going.
"We did that very well, but Bayern are smart and you have to cover a lot of ground. The second goal settled the outcome and it broke our resistance."
Bayern return to the Bundesliga with an away trip to Nuremberg next Saturday.