The former England international was hauled off at half-time in his side's disappointing 3-1 defeat at Anfield in the Capital One Cup, with the score at 1-0 to the visitors.
It was only Cole's fourth outing of the season, but it lasted just forty-five minutes and he cannot expect to feature much more after such a poor display.
Rodgers was clearly frustrated with the former Chelsea man's performance and has questioned his value to the club since his move from Stamford Bridge in 2010 - with the midfielder on a reported £90,000 a week.
"The club have invested an astronomical amount of money on a talented player and Joe had the opportunity," the Liverpool manager told the press last night.
"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."
Cole was a regular under Roy Hodgson and featured sporadically under Kenny Dalglish in 2010/11 before being sent on loan to French club Lille OSC. He performed well in Ligue 1 and was hopeful of making a positive impact at Anfield this season after being given a fresh chance by Rodgers.
EddieCThu 01/11/12 at 19:25 Doesn't sound too good for Joe.
ArtonSG8Thu 01/11/12 at 19:51 His time here is over.
NichoThu 01/11/12 at 21:58 I don't remember him playing regularly for Mr Hodgson. His time at Anfield has been frustrating and disappointing.
OlivavuThu 01/11/12 at 22:00 He played 34 times that season.
Or thereabouts. But injury and suspension were roadblocks for him.
NichoFri 02/11/12 at 13:39 13 of those were from the bench but we won't split hairs. The fact is he never achieved anything like the consistent standard expected of a player of his standing. And when you consider his remunerartion package..........
OlivavuFri 02/11/12 at 14:03 I was worried when we signed him. He hadn't performed at Chelsea for at least two years and there was good reason they were happy to let him go. He had a few good seasons under Mourinho and that was it. He is English and so overrated.
KK73Sat 03/11/12 at 04:38 Personally think he is worst than Downing. He just seems way off it. He has 18 months left on his contract surely, he needs to move on before it is too late. He needs to play at this point in his career. I have a feeling he will try hard to find a move for himself in January.
jcallen29Sat 03/11/12 at 08:22 He could join everton 
OlivavuSat 03/11/12 at 10:29 January would make sense. Let him have a free just to get him off the wage bill.
jcallen29Sat 03/11/12 at 16:56 We got him on a free although we've spent a fortune on wages. Let him go in Jan 
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