The London club are still without a point on their travels in the 2014-15 season, and remain in the relegation zone following yet another defeat on the road at Goodison Park.
A stunning strike from Ross Barkley put Everton in front and Roberto Martinez's side doubled their lead when Kevin Mirallas' free-kick took a wicked deflection off Eduardo Vargas and beat Robert Green before half-time.
That was only Rangers' third goal from eight Premier League games away from Loftus Road, but Redknapp took heart from their latest unfruitful outing.
He told Sky Sports: "I thought we played okay for 35 minutes or whatever it was. I thought we were comfortable and had good control.
"The first goal a great bit of play from Barkley, but took a deflection, and then obviously the free-kick as well.
"We kept going, but we needed a goal. The Everton crowd was edgy, I thought if ever there was a time we could come here and get a result this was it. I wasn't disappointed with how we played, I thought we played OK tonight.
"I was pleased with the performance. We pressed them well, worked hard and deserved more than we got from the game."
