QPR's relegation to the Championship was confirmed on Sunday following a 0-0 draw at Reading, who have also slipped out of the top flight.
There had been speculation that Redknapp could leave Loftus Road after only taking over at the club in November following the departure of Mark Hughes.
However, following a meeting with QPR chairman Tony Fernandes and other board members on Monday, Redknapp confirmed he will be staying in his post.
"I signed a contract here with the owner and everybody else, and they couldn't be nicer people," Redknapp told Sky Sports News. "It's not entered my mind to leave.
"I concentrated on trying to keep the team in the division, but it's not been possible and we've fallen a bit short.
"We'll try again next year to get back in the Premier League which is where we want to be."
The likes of Loic Remy and Chris Samba have been linked with moves away as a result of QPR's relegation, and Redknapp will make decisions on who he wants to keep for a promotion tilt.
He added: "We've got lots of players that we've got to make up our mind on. There are ones we want to keep and ones we want to move on.
"You've always got several players who are good enough to go and move on, and when you've got good players other clubs want to take them.
"There are other players that you want to get rid of who are difficult to shift because people don't want them because they haven't done very well.
"That's football, it's the same at every club in that situation and we're no different.
"We're positive and looking forward to now building a team in the summer to give us a chance to get promoted next year. It's a big challenge, but an exciting challenge and one I'm looking forward to."
Redknapp is aware that it will be a difficult ask for QPR to bounce back into the Premier League at the first time of asking.
"It's going to be tough," he continued. "There are a lot of good teams in that league.
"There are some great clubs in there from top to bottom with great tradition. They are big clubs, great stadiums and they all want to be back in the Premier League.
"It won't be easy, but that's where we are next year and we've got to do our best to get out of it."