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.
Steven Naismith added a third early in the second half, but Rangers showed some character and Bobby Zamora scored his first goal of the season after coming off the bench.
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."
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