The Turkey star made the move to Anfield on a season-long loan from Real Madrid last summer but failed to make an impression.
Sahin, who is currently back at former Borussia Dortmund on loan, made only 12 appearances for Liverpool before the deal was terminated in January.
And despite admitting he was proud to have represented the Reds, he remains frustrated by his treatment by Rodgers, who he claims played him out of position.
"Brendan Rodgers wanted me to play as a 10 but I do not play behind the forwards," he said.
"I spoke with him and asked him why I was playing there. It is not my real position. The boss could not answer me... still, I am not sorry about it.
"To play in the red jersey and be in Anfield is something marvellous.
"Maybe if I had not gone there I would not have been able to return to Borussia Dortmund. For that, I am happy.
"But I have left Brendan Rodgers, thanks be to God."
Sahin made his name at Dortmund before joining Real in 2011 and he admits he is happy to be back playing again at Signal Iduna Park.
"I feel well physically and mentally, everything is perfect. After returning to Germany, I feel much better," he added.