A goal from Joe Cole had put the Merseysiders ahead after Raul Bobadilla's goal cancelled out Jonjo Shelvey's opener but Elsad Zverotic equalised for the visitors in the 88th minute, denying the Reds the chance to seal progression from the groups.
"The players gave everything. The team out there was very committed against a good side," Rodgers told reporters.
"[But] you lead twice in the game, and miss a hatful of chances as well, and then to concede the goal like we did at the end was very disappointing.
"When you're 2-1 up with three or four minutes to go, you've got to control the game better. You've got to show better game management. That was the only disappointment.
"I'm not telling you anything I haven't told the players. We get the chance to shoot at one end and then in the 87th minute we're walking back.
"Oussama [Assaidi] has a go at trying to get the ball but then they work their way through to the edge of the box unchallenged. It's a disappointing goal when you analyse it.
"That's about management of the game at that stage. You're winning the game, you don't need to commit the bodies forward and leave yourself isolated.
"That's something we'll improve on."