QPR keeper Júlio César had to make back-to-back saves to deny Spurs duo Jermain Defoe and Emmanuel Adebayor in the fifth minute before the Hoops dominated the rest of the first half.
Shaun Wright-Phillips had the best chance for the west London outfit to break the deadlock when he raced onto Adel Taarabt’s pass – but the winger’s shot was deflected wide by Michael Dawson.
André Villas-Boas’ side adopted a more attacking attitude after the interval, but QPR’s defence, marshalled by Ryan Nelsen and Clint Hill, restricted the visitors to few chances.
“I see that as almost as good as the result we had at Chelsea,” Redknapp told BBC Sport.
“It was a fantastic performance from a team that worked its socks off against a great team like Tottenham, it was a great point for us.
He added: “We have to play that way [pressing the opposition]. There’s no point us trying to be open and murder teams because we haven’t got the equipment to do that.
“We have to play to our strengths and we did that at Chelsea, we went there and pressed them and closed them down, and I thought we did that today.
“César made some great saves when he had to but he wasn’t bombarded or under pressure making save after save. I felt we restricted them to very few opportunities and I couldn’t be more pleased.”
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