The 30-year-old, who earns a reported £90,000-a-week, was substituted at half-time on Wednesday night with his side 1-0 down in an ultimate 3-1 defeat as they surrendered their hold on the Capital One Cup.
It was only Cole's fourth appearance of a season which has been hit by injury and, after his error-strewn 45 minutes against Swansea, it seems unlikely he will get another outing any time soon.
Rodgers, who inherited Cole from one of his predecessors, Roy Hodgson, was frustrated with his former Chelsea colleague's display and hinted the ex-England international has not justified his salary since arriving in the summer of 2010.
"The club have invested an astronomical amount of money on a talented player and Joe had the opportunity," Rodgers told the press after the defeat by his former club, Swansea.
"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 arrived at Liverpool as a free agent and made 32 appearances in his debut season before he was loaned to then defending French champions Lille for the 2011/12 campaign.