James Chester's second-half strike was the difference between the two sides at Loftus Road, but the hosts should have earned a point in their first game back in the top flight as Charlie Austin missed a late penalty.
The Championship play-off winners controlled the first half, but failed to make it pay as the visitors defended resolutely.
Chester's header shortly after the interval secured the win for Steve Bruce's side, with Austin seeing Allan McGregor save his spot-kick five minutes from time on a frustrating day for the London club.
Despite the defeat, Redknapp was happy with QPR's start to the new campaign and expects his side to improve further as their fitness improves.
"I was very pleased with how we played today," said Redknapp. "Some days it just doesn't go your way and to get a penalty late on, to be honest if we'd have scored that I think we had time to win the game, the momentum was with us.
"But that's how it goes, some days you get the breaks and some days you don't, I couldn't fault them (his players).
"I thought in the first half we played ever so well, looked in control, good shape, passed it well, created some good chances so it was encouraging.
"We'll only get better."
The 67-year-old also sang the praises of new central defender Rio Ferdinand, despite the former Manchester United defender losing Chester for Hull's goal.
"Rio was excellent wasn't he," he added. "I thought it was almost a masterclass in how to play at the back.
"He looked so comfortable, his touch, passing and reading of the game, he's a fantastic footballer."
