They might have collected all three instead of a 0-0 draw had the Sunderland goalkeeper Simon Mignolet not managed to keep out first-half efforts from Djibril Cissé and Jamie Mackie and then a third from the substitute Shaun Wright-Phillips at the death.
His new club actually slipped a further point away from safety however the performance against Martin O'Neill's side has given Redknapp heart that QPR, with just five points and no Premier League wins heading into December, can stay up.
"I can see decent players there that need to be a team and play as a team," he said. "If we can get them to work together we have a chance. I'm happy with that display and we worked hard. I felt we got the best out of what we had. You can't do any more than that. [Samba] Diakité could be a really good player. The other lad along side him – [Stéphane] Mbia – is strong. There are good positives there.
"Listen, there are areas of the team and you can only work with what you've got. I can't pluck anyone out of the air at the moment. We have to get the best out of the players we have,
"It was good to be back, I kept Martin quiet" he added. "He didn't jump around too much. Yes, it's going to be tough, we mustn't kid ourselves. You look at the position we're in. It's very, very difficult.
"Confidence has got to be a bit shot when you're in that situation. You only have four points. You keep telling them they're good and they will keep going. We have an important match with Villa on Saturday. We have to make Loftus Road a bit like Portsmouth used to be. It's a small stadium, we want to make it intimidating and get the fans right behind us."
"We worked hard. We well deserved a point. We had some good opportunities ourselves an good have scored ourselves late on. There was a lot of pluses and I liked the look of us. The midfield looked strong. The three lads in there were powerful. There were some good points came out. I feel more optimistic than I did on Saturday.
"The keeper [Julio Cesar] has torn a groin. He is a good pro. You can see why he's played at the very top. He went off and Robert Green made a great save. We're lucky there, we have two great players."
For Sunderland there were jeers from the crowd at the final whistle. They have won just four times in their last 27 Premier League games and their poor form has added a new sense of unrest to the Stadium of Light.
Losing their captain Lee Cattermole to a knee injury early in the match did little to settle things either. Cattermole, who had already shaken off a knee injury to start the game, departed with just seven minutes played having damaged the other knee in a 50-50 challenge with Diakité.
"It was a rather frustrating evening," said their manager Martin O'Neill. "It was tough for us. Losing Cattermole so early in the game disrupted us. Even so, it's a handicap you have to overcome. It was just a frustrating evening.
"It was his other knee he hurt, in the blocked challenge. He is in a lot of pain. It would be a big blow. I thought it was the same knee but it is the other one.
"QPR would be buoyed by Harry's arrival. They had renewed spirit about them. It became a tough evening. They led Manchester United and took the lead against them. I knew the game was going to be difficult. It is difficult for us at this moment because we need to play with more confidence.
"The crowd gets edgy and I think this is a sign of character as much ask anything else. You have to play the ball that you choose, and not the one the crowd want you to play. Ours wouldn't be the only crowd that would be getting anxious about such things.
"The lads said it was really tough last year as well around this time as well. The matches the boys played before Steve [Bruce] departed, it was particularly tough when they lost the game against Wigan the lads were saying. We have to tough it out."
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