Agger ended an eight-year spell with Liverpool in August by returning to former club Brondby in a reported £3 million move.
The Denmark captain was second choice to Mamadou Sakho and Martin Skrtel in central defence last season as Liverpool finished second in the Premier League under Northern Irishman Rodgers.
And Dejan Lovren's close-season arrival from Southampton pushed Agger further down the Anfield pecking order.
However, Agger revealed that a failure of Rodgers - who he went on to describe as "an extremely competent coach" - to appreciate his contributions, rather than a lack of first-team opportunities, was the key factor in his decision to move back to his homeland.
"Let me put it this way - me and the manager were perhaps not on the same page for all of last season. For most of last season at least," Agger told Danish TV programme Onside.
"There was some distance between us and for me that was enough. I didn't feel that he appreciated the things I contributed. And when I feel that, then it is time to move on.
"Maybe where it went wrong between me and him is that I am very direct. I say things as they are, and also expect that people are [that way towards] to me. Maybe it's wrong to expect that."
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