Brett Holman scored the opening goal for Villa with a powerful strike but Jamie Mackie headed home to secure a point for the R's in Redknapp's first home game in charge.
"There's no shortage of spirit and no shortage of effort and I thought we played ever so well. We just couldn't get that second goal," Redknapp told Sky Sports News.
"Villa kept the ball in the second half. That made it difficult as they knocked it around without going anywhere but I don't remember them having a real opportunity second half.
"We just have to keep going. We are in a difficult position, there's no doubt about that.
"We have just got to believing, work hard and try and get that first win. That's we need to get us up and running."
Redknapp admitted he was pleased with the positive response he got from the Loftus Road crowd but insisted it was matters on the pitch that were crucial.
"It was good but the most important thing is the game. I thought we played well today after a difficult start," he added.
"After we went one-down we played some good football and hit the woodwork several time. We had all the chances really and I thought we deserved to win.
"We needed a win today but it didn't come and we will have to go again next week and get that first win under our belts."
Redknapp also confirmed that Stephane Mbia did not suffer serious injury despite having to be stretchered off after colliding with Gabby Agbonlahor.
"He's OK, he's just got a bit of a neck injury. He's gone for a check-up but I don't think there are any problems and he should be fit for next week," he said.