Rangers became the first team in Premier League history to fail to win any of their first 16 games in a season when they were held to a 2-2 draw by Wigan at the DW Stadium this afternoon.
Redknapp's side exceeded the previous record set by Swindon, who were relegated in the 1993/94 season, while the last team to reach 16 games in the top flight without winning were Sheffield United in 1990/91, before the Premier League era began.
Redknapp is still unbeaten since taking over from Mark Hughes having drawn all his three games and he has already been talking about possible January targets.
Rangers have struggled despite being one of the highest spenders in the Premier League in the summer and Redknapp implied he would consider relegation a certainty if they head into January still winless.
The R's boss said: "It we don't win a game or two then I wouldn't ask them to spend any more money. I think it would be unfair to the owners.
"I wouldn't tell them to go and spend big money on a couple more players if we're that far adrift. You've got to be realistic.
"I'm just hoping we can get that win or two and then I'm sure they'll have a go because they've had a go in the summer. They've done whatever was asked of them and look what they've ended up with.
"It's difficult. I can only work with what I've been given. It's like you've dealt me a hand of cards and this is what I've got. We've left ourselves with a squad that's got no balance to it, we've got no strikers."
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- Premier League