Spurs' home draw against Villa on Saturday evening means that they surrendered fourth spot to Liverpool, who won 1-0 at home to Everton earlier in the day.
However, Redknapp believes that Spurs, Villa and Manchester City (who lost 2-1 at Hull) still have high hopes of attaining the coveted Champions League spot.
"Obviously it was a big result for Liverpool," Redknapp said.
"They ground out a result. It's their weekend this week, it will be somebody else's next week, somebody else's the week after.
"Of course it's going to be tight, it's going to go all the way to the wire.
"You didn't see Manchester City getting beat at Hull, not many people would have tipped that one, would they?"