Spurs looked certain to qualify for next season's Champions League until February but are now in a shootout with Arsenal, Newcastle and Chelsea for third and fourth place going into the final week of the campaign.
Redknapp told BBC Radio Five Live: "We're a good side. If we're bold in the summer, we can build a team again that can be right there again next year.
"The league is changing and a top-four position is very difficult to achieve."
Tottenham are a point behind third-placed Arsenal going into Sunday's final game of the season against Fulham.
Only a top-three finish will guarantee Champions League football, with fourth coming into play providing Chelsea do not win this month's final against Bayern Munich.
It is a nailbiting end to what has been a rollercoaster season for Spurs and Redknapp, who was cleared of tax evasion in February and made favourite for the England job before it went last week to Roy Hodgson.
He said: "I'll be glad when next week is over. It's been a long old season.
"I just want to get in the Champions League and have a break and get away for a few days.
"It has been a hard year for me personally. What I went through with the court case was the most difficult thing I've ever faced in my life.
"It definitely takes a strain on you. I do tend to get on with things but there's no doubt it has an effect."
Redknapp reiterated he bore no grudges over the Football Association's decision to overlook him for the England job.
"It was no hassle to me at all," he said.
"It never really bothered me. When I heard that Roy had got the job on Sunday night, I went out.
"I didn't go out feeling, 'Oh my God'. I woke up the next morning and I was quite relieved in a way that I didn't have a decision to make."
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