Cole made his first start for the Reds since coming off injured in their 3-1 victory over Gomel in the Europa League in August and spurned the best opening of the first half when his tame header failed to trouble Swansea’s Gerhard Tremmel.
The 30-year-old, who spent last season on loan at Lille, is on a reported £100,000-a-week after he was signed by Roy Hodgson on a free transfer from Chelsea in June 2010.
“The club have invested an astronomical amount of money on a talented player and Joe had the opportunity,” said Rodgers.
“He has been back fit a couple of weeks and his opportunities have been limited but you have to see. I thought it was difficult for him, it was too slow and it wasn’t what I would expect from a team I tried to set up to be dynamic.”
Goals from Chico and Nathan Dyer put Swansea in command with 17 minutes remaining, and although Luis Suárez’s strike offered Liverpool brief hope, Jonathan De Guzman secured the win in added time.
Despite Cole’s poor performance, Rodgers reserved praise for former Swans midfielder Joe Allen and veteran centre-half Jamie Carragher for impressing in the cup loss.
“Joe was incredible,” added Rodgers. “You can see he has come out of that Swansea team and into our team with his brightness and his cleverness. He was virtually playing on his own in the midfield in the first half.
“I thought Jamie Carragher was outstanding. He kept going tonight and kept driving. Young Raheem Sterling came on and added brightness and so it’s another game for me to take away and analyse.
“We’ve got a very small squad and we have been playing in three competitions. I have rotated the side, like in previous games, to look at younger players and fringe players and to give people opportunities to come into the team.”
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