The 65-year-old was appointed at the Loftus Road helm in the immediate aftermath of Mark Hughes' sacking with the remit of keeping the Hoops in the Premier League.
It is a big task for Redknapp, with the west Londoners languishing bottom of the table and their winless start to the season extended to 15 matches with Saturday's 1-1 home draw with Aston Villa.
Asked if keeping QPR up would be his finest feat, the former Tottenham, Portsmouth, Southampton, West Ham and Bournemouth boss said: "Of course, absolutely from where we are. We will try. It is going to be hard.
"I've taken a big task on here. I know what I've taken on, I'm not a fool. It's going to be difficult but you can only give it your best."
Redknapp is not new to such a situation and has masterminded several previous relegation escapes, although he failed to do so with Southampton seven years ago.
"It always creates anxiety when you're bottom of the league and can't get a win," the QPR boss said.
"Football is like life - it is about confidence. When things are going well, you win games and you don't know how you won. You come off thinking 'we were rubbish today but we won again'.
"Sometimes, like we are at the moment, you play well but you can't get the win and that's how it goes.
"They have shown a good attitude. They've trained hard, worked hard. They've all been good, they're good lads. We just need a win, don't we?
"We could have got that win on Saturday with a bit of luck. Clint Hill's header I thought was dropping in and if that goes in it's a different game.
"We would be back in there, chasing the pack, but we couldn't quite get those three points."
Shaun Wright-Phillips was recalled to the starting line-up against Villa and produced a far better display than many previously seen in a QPR shirt.
"I think confidence is the key for him," Redknapp said. "He has to play with confidence.
"He made some good runs and great ones in the first half, where he should have scored and then hit the post.
"But he bent his runs in off the line and looked lively. He has done well in training and I gave him a chance."