Tottenham 2 // West Brom 2
Redknapp's men looked set to earn the victory that would have taken them ahead of fourth-place Manchester City when Jermain Defoe scored his 100th Spurs goal with 25 minutes left to put the hosts 2-1 up.
However, a superb lob from the West Brom substitute Simon Cox that found the back of the net with nine minutes left meant that the Londoners settled for a point.
City will move four points clear if they beat lowly Blackburn on Monday night and Redknapp has the headache of a tough run-in that includes matches against Chelsea and Liverpool. But he remains optimistic about his side's chances.
"It's going to be difficult but it's still all to play for," he said. "I find it hard that now everyone expects us to be in the Champions League. Tottenham had never been in it before until this season and suddenly it is like, 'We have to be in the Champions League.'
"Manchester City have gone out and spent God knows what to get above us. Arsenal, Manchester United and Chelsea are there every year, Liverpool will be there next year. It's difficult to get fourth. It has been a great season but it's not over yet."
Peter Odemwingie's 13th goal of the season gave the Baggies the lead before Roman Pavlyuchenko equalised in the 27th minute with a well-taken strike that flew in off Scott Carson's far post.
Roy Hodgson has now taken 13 points from his eight matches in charge to propel the West Midlanders to 40 points and the brink of safety. He said the club "might need a point or two more.
"It was a splendid result to come back from 2-1 down.
"It's given us what looks to be an important point."