The Hoops were undone by two second-half goals from Lars Stindl and Andre Hahn, which leaves them bottom of the Group C standings and with their hopes of progression in the Champions League in tatters.
Kolo Toure was at fault for both Gladbach goals, which the experienced defender was quick to take the blame for, but Rodgers was not willing to pick out any individual player following the costly defeat.
"We were beaten by [a] better team; you can't argue with that," he told BT Sport. "They were just sharper and quicker and that's the level we aspire to.
"When a game is going like that you don't want to gift anything and, unfortunately, we gave away two gifts. Kolo Toure has been outstanding since he got here and nobody is attaching any blame to him."
Celtic return to European action on November 1 with a trip to face tonight's conquerors Gladbach, but before then is a clash with arch-rivals Rangers at Hampden Park in the Scottish League Cup semi-final.