Rangers maintained their unbeaten start to the Sky Bet Championship season after a Charlie Austin penalty 15 minutes from time separated the sides.
The QPR boss admitted his side were fortunate to get the three points at Huish Park - but reserved praise for Dunne who helped the league leaders notch a sixth successive clean sheet.
Redknapp said: "It was a tough three points and I thought Yeovil were unlucky to lose the game. They played well and put us under pressure.
"I've been around long enough to know that you rarely come to places like this and turn teams over. Yeovil will give anyone a game as this isn't an easy place to come.
"They created chances and we stopped passing the ball in the second half. I thought we controlled it in the first half, but then they were on top of us.
"We defended well again and dealt with a lot of set plays late on. Richard Dunne was immense, and so was Rob Green.
"When I brought Richard into the club this summer I slept a lot easier because I knew we were signing a top player, a captain of his country and a Premier League player. If he stays fit, we have got a great centre half.
"The problem I've got is that I only have one striker. We didn't create a lot of chances, and without Charlie Austin we would be in trouble.
"We lost Andy Johnson and Bobby Zamora has had an operation, so it's something we are working hard to try and find somebody to come in."
Despite seeing his side lose a fifth consecutive match on home soil, Yeovil manager Gary Johnson was proud of his team's display.
Johnson said: "I'm going to be happy tomorrow because when I watch the video I will see we outplayed a quality team.
"We can't keep being unlucky and we don't want to be relegated as the unluckiest team ever.
"We have to start putting our opportunities away, but we're not always going to have Robert Green in goal against us.
"We need to keep plugging away and believing in our game. They've been around at this level for a long time, but we can go home happy in the fact that we gave more than we got.
"The players will be disappointed but we can't forever wrap them in a comfort blanket.
"We've got to improve in certain areas and we will be relentless in our coaching and our attitude. It's not our football that's letting us down at the moment."