Despite plenty of endeavour, QPR were unable to get the breakthrough which Redknapp felt would have seen them go on to win the match.
The key moment came just before the hour when QPR were awarded a penalty for a trip by Norwich keeper Mark Bunn on Jamie Mackie.
However, Adel Taarabt, who had been Rangers' most creative player, saw his spot-kick well saved by Bunn.
Both keepers produced a string of fine stops, with Julio Cesar also doing well to deny Wes Hoolahan from close range and tipping behind a 25-yard curling effort from Robert Snodgrass.
Redknapp said: "I felt if we had scored the penalty, we would have gone on and won the game.
"Of course we need wins but we could not have tried any harder - we gave everything we had.
"I felt when Bobby Zamora came on, he made a difference for us, but he cannot play for 90 minutes because of an operation on his hip.
"Once he stops, it just clamps up on him. Getting him through half a game is a miracle. If I had him fit, it would be a different team."
Redknapp remains positive for the challenges ahead and added: "We just have to keep going."