Despite extending their unbeaten run to five matches, the Hoops are six points of safety.
Redknapp knows his side - which included £12.5million deadline day signing Christopher Samba and on-loan Tottenham midfielder Andros Townsend - failed to make the most of a golden opportunity to close up on the sides above them when Adel Taarabt saw his second-half penalty saved by Mark Bunn.
"We have not lost a game since the turn of the year, which is not bad if you look at the matches we had, because they were not easy," the QPR boss said.
"If you get something at Chelsea, you think it was a miracle, then you come up against Tottenham at home, away to West Ham, here against Manchester City, they are all tough.
"However, Norwich at home was one I looked at and thought 'we have to go for it and get a win'.
"But I couldn't have asked for any more, we just needed a break.
"If we had converted the penalty, we would have won."
Redknapp hailed Samba as a "colossus", the centre-half having played when "only 40% fit" following his move from Russian side Anzhi Makhachkala, where he had not played since November because of their winter break.
The QPR manager was also more than happy with the contributions of Townsend, who forced another good stop from Bunn with a late 25-yard strike, while Jermaine Jenas - who also played for him at Tottenham - produced a solid display after coming on as a substitute.
"It has been no problem - Samba played like he had been here all of his life, so did Townsend," Redknapp said.
"We have only had the two new boys in really, and they were arguably the best two players on the pitch."
Striker Loic Remy is set for a spell out with a groin injury picked up in training on Friday, the extent of which should be known by the start of next week.
With Bobby Zamora struggling for full match fitness after a hip problem, Redknapp accepts his attacking options are limited.
"When Bobby came on, he pinned Norwich back, we dropped balls into him, he could flick things on and play people in," the QPR boss said.
"He is just not capable of doing it for more than 35 minutes at the moment."
Norwich, meanwhile, maintained their seven-point gap over the relegation zone with a well organised display.
Boss Chris Hughton reserved special praise for Bunn, in goal because John Ruddy is sidelined after needing surgery on a thigh injury.
Hughton said: "Unfortunately for Mark, he has been here in a period where form has dipped a bit and in particular we have had a couple of big defeats, conceding four at home to Manchester City and five at Liverpool.
"Overall, though, Mark's game has been good and we certainly needed him to be here."
"The last two results have consolidated things a bit for us. Now, for us it is about pushing on again, because there is that difference between picking up draws and getting those valuable wins which would take us that bit further away.
"At the moment we are not doing too much wrong, but just need that little more offensively to be able to get the goals we need."
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