Sahin, 24, was originally on a season-long loan at Liverpool from Real Madrid this season but the deal was terminated in January before he returned to his former club Borussia Dortmund on an 18-month loan deal.
The Turkey international made 12 appearances for Liverpool but only managed to complete the 90 minutes four times, three of which were in the Europa League.
He told AS, as cited by ESPN, that Brendan Rodgers had played him out of position as a number 10 but he felt his best position was deeper in midfield.
"I did not fail at Liverpool," Sahin said. "Brendan Rodgers wanted me to play as a '10'. But i do not play behind the forwards. I spoke with him and asked him why I was playing there. It is not my real position.
"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 said he had a much better relationship with Blancos boss Jose Mourinho and had been impressed by the Bernabeu side's recent form, especially the 2-1 Champions League win at Old Trafford.
"I believe the game against Manchester United is very important for Madrid. Now they are in a perfect position. The truth is Madrid are one of the big favourites for the Champions League."
Although still being used mostly as a substitute since his return to Germany, Sahin seems much more at home with Dortmund and believes they are capable of challenging for the Champions League.