While Rodgers' men challenged for the Premier League title, Agger was often overlooked for a starting spot in favour of Mamadou Sakho and Martin Skrtel, having also suffered with injuries.
With the Denmark international having previously stated his intention to ignore speculation linking him with a move to Barcelona, Agger revealed his frustration, stating Rodgers did not feel he was "good enough".
He stopped short of confirming any plans to leave Anfield but warned he would not be content to be a substitute next season.
Asked about being benched for the crucial late fixtures against Chelsea and Manchester City, he told Ekstra Bladet: "It definitely wasn't great. But I don't make the decisions. I think it is because the manager doesn't think that I'm good enough.
"(My future at Liverpool is) up to the manager. I can't go and put myself on the team-sheet.
"I'm no-one's third choice."
Agger moved to Liverpool in 2006 from Brondby and has made 232 appearances during his time with the club - winning the FA Cup and the League Cup.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.