Redknapp feels that Tottenham are wasting their big opportunity, as they have not done enough in the transfer window.
Spurs have finished in the top four comfortably for the last two seasons, and looked to be one of the biggest contenders for the Premier League title.
However, a lack of spending appears to have hurt Mauricio Pochettino’s side this season.
Spurs have taken just five points from the last 18 available to them, and are currently sat in sixth place in the Premier League table.
Pochettino’s side’s place in the Champions League next season is now under threat, and Redknapp feels that Levy should take some of the blame.
“This should be a time when they should be looking at all the best players in Europe,” he said. “[Players will be saying] ‘How much are you going to give me Mr. Levy?’ No, I’m not going to sign for that, because I know in the other part of North London I’ll get three times that.
"You can’t keep going for the next cheap player. It’s not as easy as that. You have to pay up and look big, otherwise it’s soon going to change there.”
Spurs did add to their squad in the summer, but many of their new recruits have failed to make much of an impact.
Juan Foyth is one for the future, while Fernando Llorente has struggled up-front.
Davinson Sanchez, who came in as Spurs’ record signing, has impressed - but there is a feeling that Pochettino’s side have gone backwards rather than forwards from last season.