A youthful Reds line-up looked set to progress until Elsad Zverotic's stunning equaliser on 88 minutes grabbed a share of the spoils for the Swiss side.
That leaves Liverpool needing to take something from the final group game away to Udinese and Cole, who scored a goal and set-up another, believes they should not find themselves in such a position.
"It's disappointing. It was just the game management at the end," he said in an interview on ITV.
"We need to see the game out. Maybe we had a few young players on the pitch but we should have killed the game of.
"Fair credit though it was a good finish from their kid."
While Cole was left deflated he could reflect on an impressive night personally in his third game back from a long-term hamstring injury.
Cole set up Jonjo Shelvey's 33rd-minute opener with a lobbed assist across goal before he put Liverpool back in front with 18 minutes left.
The veteran midfielder's place at Anfield has been questioned in the recent past but he believes he still has a future under new boss Brendan Rodgers.
"Of course. I was a good players at West Ham, Chelsea and Lille and I think I can be a good player a Liverpool," he said.
"I'm getting stronger with every game. It is normal that a player wants to play all the time.
"It was my third game back from a hamstring problem and I felt good.
"On a personal note it was quite good. The overall sense though is disappointment that we didn't see it out in the end.
"But the young lads especially have been terrific this year. We just keep going."