Second-half goals from Maxi Rodriguez and Martin Kelly sent the Reds through at the expense of Andre Villas-Boas' side, who suffered at the hands of referee Phil Dowd.
The official failed to give an early penalty the way of The Blues following Sebastian Coates' slide tackle on David Luiz, who was subsequently booked for simulation.
"There were a lot of penalty decisions, we had one of two," Turnbull said.
"I haven't seen them but I know we had one and they were claiming one or two and the game is so quick it's difficult to see whether or not they are or they aren't obviously the referee gave one and that's the one that matters."
The hosts rode their luck in the first half when they conceded a spot-kick of their own, when Alex handled Jose Enrique's cross, only for Andy Carroll to drive straight at Turnbull.
It was the sixth spot kick-conceded by the club this season, and despite four of them having failed to find the net, Turnbull says the errors must be irradiated from their game.
"It's been an eventful Carling Cup run and unfortunately it's over," he added. "I think in every game we've conceded a penalty so it's difficult to say but I just think we didn't perform tonight and Liverpool deserved to win."