Sergio Aguero opened the scoring after four minutes before Aleksander Kolarov's free-kick made it 2-0 at the break.
Yun Suk Young allowed Aguero to score his second after losing the ball and the Argentine completed his hat-trick from the penalty spot.
James Milner made it five and David Silva rounded off the scoring to relegate QPR.
He said: "Yes. I really do want to stay. It's a club that I've taken to my heart and I really want to be here."
He explained: “All the mistakes and errors we have made throughout the season played out in 90 minutes yesterday.
“We just were not good enough and that has been the case throughout the campaign. There are loads of questions that needs answering.
“Ultimately we did not have the quality to stay up. It is a difficult one to take and we have to apologise to our fans.”