Harry saw his side twice take the lead before having to stage a comeback with a third, and he was pleased, in the end, that his side won a point. "It was a very important result," he said. "I felt at half time we'd go on to win; I thought we were better than them in the first half.
"But they came out flying in the first 20 minutes of the second half and it was difficult. We were sloppy with some of our defending for the goals but they were always a threat.
"To come back from 3-2 down in the end was good. We could easily have dropped our heads but we didn't, we kept going. In the end it was a fair result."
Redknapp saw two of his five deadline day signings score goals, Kevin Doyle and Modibo Maiga. "It was encouraging," he added. "Kevin Doyle's won the fans over straight away today. Not only because of his goal but his work rate is fantastic. He's put a shift in today. That's Kevin Doyle; he gives everything and he'll do that week-in week-out for us.
"Andy Johnson worked hard up there with him and then Modibo came on and grabbed a goal as well so that was encouraging.
"If I'm being totally honest they were both gambles. Kevin hasn't been scoring goals for Wolves and neither has Modibo so we were taking a chance on both players but it paid off today."
On their promotion hopes, he added: "It's going to go right to the wire, it's going to be close.
"They're a good team, Burnley. Their work rate is fantastic; they've got good players and a fantastic young manager. They'll be right up there at the end.
"But there's not only ourselves and Burnley. Leicester are obviously flying and there's lots of other teams that are all very good. It's going to be a tight end to the season but at least we're up there. We've got as good a chance as anybody."
Dyche, really delighted with our second half performance, said: "It's a big ask to come down here and win, as suggested by the stats this season, but I thought my lads were terrific.
"The energy, passion to win and also the quality were there and some of our play today was tremendous against one of the top teams and most powerful squads and clubs in this division.
"But our mantra is to go to win and I thought there were massive signs of that today, because we didn't do anything other than go for the win.
"We had a sticky first 15 minutes and all of the goals we conceded were soft, in different ways, which is unlike us. I am disappointed with the two corners because we normally do so well with that, but that's a minor thing. It's not a recurring one and that can't and won't detract from that performance.
"We showed our intent and if Junior gets a gust of wind at the end, it wins it.
"I thought we just about did enough to edge it, but I don't over-think the results because it's about performances and if you keep putting them in, the wins will come."