For large parts of the season Spurs were challenging champions Leicester City for the title, but a late season implosion saw their hopes fade.
It appeared as though a consolation of prize of finishing above Arsenal for the first time since 1995 was on the cards.
However, Mauricio Pochettino's men took just two points from their last four matches and a 5-1 hammering at relegated Newcastle United on the final day of the season saw Arsenal pip them to a runners-up berth.
But Redknapp - who managed Tottenham for four years between 2008 and 2012 - believes his former club are in a stronger position than Arsene Wenger's men.
"Wenger deserves enormous credit for finishing above Tottenham in the league, but I know which squad I would rather have," Redknapp wrote in his column for The Telegraph.
"Being brutally honest, Arsenal are very lucky to have finished the season second and Arsene needs to buy some players over the summer to get anywhere near Spurs.
"There will be a feeling of real disappointment around the place, but when the dust settles it's still been an outstanding season for Spurs.
"They have qualified for the Champions League, which is a huge thing for their chairman, Daniel Levy, and done it without having to go through the knockout stages.
"Arsenal need to buy, there is a lot of work to do. They desperately need a new centre-half and another striker to take them forward. Too many times this season they've been suspect in certain areas, whereas I can't see any real weaknesses in the Spurs team.
"Spurs will be hurting as they reflect on finishing third but, at the moment, their future certainly appears brighter."