Spurs' 1-1 draw at home to Blackpool means Manchester City will have fourth place and the final qualification slot all but wrapped up if they beat the London side at Eastlands on Tuesday.
And Liverpool will push Tottenham out of fifth place anyway if they avoid defeat at Fulham on Monday - with Redknapp and Co also due at Anfield this coming Saturday.
"It's going to be very difficult, obviously," he said. "We haven't been able to win games in the last month or so. But it takes some doing to get in the top four anyway. We have only done it once before. It's not as though we do it every year and people have to understand that."
A well-taken equaliser by Jermain Defoe shortly before the end of normal time minute spared Tottenham from a defeat, with a 76th-minute penalty from Charlie Adam having put Blackpool in front.
Adam, only 70 seconds before scoring, had seen a spot-kick saved by goalkeeper Heurelho Gomes, who immediately conceded another, and the Scot made no mistake second time around.
The Blackpool playmaker, a Spurs target during the January transfer window, was also involved in a challenge that hurt Gareth Bale, with Tottenham's star winger carried off on a stretcher and taken to hospital for a scan.
Redknapp was hopeful the injury was not serious.
"He has done his ankle - it looks quite bad," he said. "I'm not sure if he has done his ligaments. It looked a bad challenge but that's how it goes. It might just be a twist."
The draw lifted Blackpool out of the bottom three, ahead of Wigan on goal difference, and manager Ian Holloway was delighted with a point even though he had been so close to all three.
"That was more like us," he said. "I feel like we are back on track - let's hope it's not too late.
"It's all about us progressing and that's four points we have taken off Tottenham so I have got to be happy with that. The lads were disappointed but I wasn't.
"It was a great game of football and I'm just relieved we look a good side again because I would have hated our season to just peter out and be useless -- and we're not.
"We have still a hope (of avoiding relegation) with two games left and that is all you can ask. I still believe we can perform an absolute miracle."
Holloway, who is hoping last-day opponents Manchester United will have wrapped up the Premier League title by then, also produced a vigorous defence of Adam, especially after Kevin Keegan, a pundit on the ESPN television channel that broadcast the game live, had claimed the tackle had been malicious.
"Everybody is entitled to their own opinion but Kevin should know the lad like I know him," Holloway countered.
"He almost came to Spurs so why would he want to hurt anybody? He hasn't got that in him.
"Hasn't Kevin ever been slightly late with a tackle? This level is so quick. On a beautiful surface Charlie tried to get there and it was genuine. So I'm disappointed Kevin said that.
"I thought Charlie was absolutely pole-axed by William Gallas and that was only a yellow card so as long as the referee was consistent, which he was, then who am I to judge him?"
Short link: