The Scottish champions went into the game unbeaten domestically and still on a high from the encouraging 3-3 home draw with Manchester City last month.
The Bundesliga side travelled to Glasgow without a point in two games to add to the confidence around a packed Celtic Park before kick-off, but the slick-moving visitors deservedly won with second-half goals from captain Lars Stindl and striker Andre Hahn.
The defeat left the Hoops chastened and with one point from a possible nine ahead of the return fixture in Germany in two weeks' time.
With Group C leaders Barcelona and Manchester City still to play, even a Europa League spot looks a tough task for Celtic.
"It is very difficult of course," said Rodgers.
"It was always going to be tough away at this level and home games were going to be important for us.
"So it wasn't to be but we will play the remaining games now, obviously the next game will be against Monchengladbach.
"We expect it will be tough again and we will have to do the very best that we can."
Rodgers defended 35-year-old centre-back Kolo Toure, who was at fault for both goals after conceding possession.
"He is a guy who is very mentally tough and he will recover," added Rodgers, while admitting his side were beaten by a superior team.
"I thought the best team won, I don't think there is any argument about that.
"My players gave absolutely everything but they were up against a top side.
"Our only disappointment is the two goals - they didn't create so much even though they looked dangerous on the counter attack which a lot of the German sides will.
"We gifted them two goals really.
"We had some good spells as well but we were beaten by a side who are very good, technically strong, fast, with good power and who have quality.
"We have no complaints."
Source : PA
Source: PA