Sahin joined the Reds from Real Madrid on a season-long deal in August but the agreement was terminated in January after the Turkish playmaker made just seven Premier League appearances.
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"I did not fail at Liverpool," Sahin told AS. "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.
"The boss could not answer me... still, I do not regret it. To play in the red jersey and at 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, thank God."
Sahin insisted that his relationship with Jose Mourinho remains healthy despite his lack of opportunites in Madrid before adding that recent results over Manchester United and, domestically, Barcelona prove los Blancos' credentials in the Champions League.
"We speak often on the telephone," he added. "We chat about football and life. The boss feels good. I believe the game against Manchester United is very important for Madrid. Now they are in a perfect position.
"People talk more about [referee] Cuneyt Cakir's decision [to send off Nani] than Madrid's performance, but Madrid played a very good game. They are going very well. It is not easy to beat Barcelona twice. The truth is Madrid are one of the big favourites for the Champions League."