Rangers are now without a win in five matches and needed a rare Jermaine Jenas goal to secure a 1-1 draw at home to Leeds.
The stuttering pre-season title favourites are now facing the prospect of the play-offs having slipped off the automatic promotion pace.
They fell behind to Ross McCormack's 24th goal of the season but midfielder Jenas ensured they avoided a fourth successive defeat when he slotted in the equaliser just before half-time.
Both teams had chances to win it with Leeds debutant Connor Wickham twice going close and Jack Butland saving well from Armand Traore before Clint Hill's stoppage-time strike was ruled out for offside.
But Rangers boss Redknapp was left to count the cost of an injury list which includes the likes of Niko Kranjcar, Matty Phillips, Danny Simpson, Andy Johnson and top scorer Charlie Austin.
"Obviously you want to win your home games," he admitted. "We came out in the second half and had a great chance through Traore. But the game faded away after that.
"Am I encouraged? Absolutely. I've not been disappointed with them in any of the games. You need to win football matches but it's not through lack of effort.
"If I was picking my best team today I think I've got six or seven players missing. It's very difficult, these are key, key, key players.
"We will keep going and if it means going through the play-offs at the end of the year we've got to make sure we get there and then we'll go from there."
Redknapp came out fighting this week, denying suggestions that his position is under threat while claiming their recent form is nothing more than a 'blip'.
However, that blip was in danger of turning into a full-blown crisis when McCormack fired Leeds ahead with a deflected free-kick, just moments after he had missed a penalty.
The visitors were given a 10th-minute spot-kick when Richard Dunne's clumsy challenge sent McCormack tumbling in the penalty area but his weak effort was saved by Rob Green.
However, the in-form frontman made amends four minutes later with a curling free-kick which clipped the Rangers wall on its way past Green.
But Jenas snatched a point for the hosts with his only second goal of the season, firing home from the edge of the area a minute before half-time.
Leeds remain in a state of flux with Massimo Cellino's controversial takeover yet to be completed, but boss Brian McDermott remains as upbeat as ever.
"You'd take a point before the game here, but as the game panned out it was disappointing not to take all three," he said. "We should maybe have killed the game off in the first half.
"But it is what it is, another point on the board and I just want positivity around Leeds United. We haven't had much lately.
"We are still waiting for the takeover to be completed but it is a much calmer place now."