Villa took the lead when Ciaran Clark’s shot from 25 yards took a wicked deflection off William Gallas and looped over Brad Friedel 10 minutes before the break.
Spurs were reduced to 10 men in the 48th minute when Danny Rose was given his marching orders for sliding dangerously into Alan Hutton.
But the Londoners equalised from the spot through Emmanuel Adebayor after Richard Dunne fouled Sandro.
The result leaves Spurs trailing third-placed Arsenal by a point in fourth ahead of the final round of fixtures next weekend.
“We dominated the second half but we couldn’t get the second goal,” Redknapp told the BBC. “It’s all to play for next week there are so many permutations.
“If we’d won today we’d have taken Newcastle and Chelsea out of the equation so we wanted three points but you can’t always have what’s ideal.
“Once you go down to 10, five minutes into the second half, you’ll take a point all day long. I thought we put a real shift in I couldn’t have asked for any more.”
Meanwhile, Villa boss Alex McLeish admitted his delight at the result which all but guarantees his side’s Premier League safety.
“It is a relief there’s no doubt,” he said. “It’s been a trying season pretty much from start to finish and when you start to lose key players it makes it very difficult.
“We have blooded young players and hopefully it will stand them in good stead.
“The main thing we focused on was attitude and in that first half I thought they we excellent. Home form has been a problem we gave Tottenham a really good game.”
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