The White Hart Lane side have suffered recent defeats to Arsenal, Manchester United and Everton, but draws against Stoke and Chelsea have steadied the ship.
Redknapp feels that despite the fact his men are three points behind their north London rivals in the race for third, they can still pip the Gunners before the end of the season.
“It is tough this year. Manchester City, with the money they’ve spent, are a certainty and United too,” he told Mirror Football.
“Arsenal have been there every year, Chelsea, and Liverpool, who you thought would get stronger, mean it was going to be even harder to make it this year.
“A month ago we were nailed on, so it would be a bigger blow if we don’t make it. But I don’t think third is out of reach, now.
“I enjoyed playing in the Champions League last season – but it’s not like it’s been part of my life or part of Tottenham’s life. They’ve not been used to it.
“Whatever happens, you need to improve every year. If Tottenham want to do it again next year, we have to improve.
“These top teams are not going to stand still, they are going to improve their teams. Man City will, and United and Arsenal have made plans to bring big players in,” he concluded.
By Gareth McKnight