Rafael da Silva and Ryan Giggs both scored in a comfortable victory for the Red Devils, which left the Hoops trailing 17th-placed Wigan Athletic by seven points.
“There are enough games left – it is still wide open,” said Redknapp.
“We have got to go to Villa, we have got to go to Reading and we have got Wigan here. I still fancy us.
“We’ve got nothing to lose, everyone thinks we are gone. But you can change it so quickly.
“At Portsmouth in 2006 I had a crap team and we got 20 points from 10 games and stayed up. It ain’t impossible.”
QPR face Southampton at St Mary’s next Saturday in a clash that sees Redknapp take on his former club on the weekend of his 66th birthday.
He was unable to guide the Saints to safety in 2005 after leaving Portsmouth before returning to Fratton Park for the 2005-06 campaign.
And Redknapp is expecting to receive plenty of stick from the home supporters next weekend.
“It is my birthday next Saturday and I thought there is no better way to spend it than getting 90 minutes of abuse at Southampton.
“They’ll all be calling me ‘Scummer’ for my time at Portsmouth. I thought that would be a great way to spend my birthday!”