Spurs haven't finished above Arsenal since the 1994-95 season, famously losing to Newcastle last year to finish third despite looking like potential title winners for much of the campaign.
Despite being ahead of the Gunners in the Premier League table in 2016-17 on goal difference, Keown believes that Spurs are still lagging far behind his former club.
“They’re 10 years behind Arsenal,” he told BT Sport. “The Wembley effect, we did that, and it was never going to be successful for them.
“I don’t think Spurs fans should get too far ahead of themselves. They have a smaller squad, and that’s due to financial constraints.
“They’re building a brand-new stadium. We’ve already heard about that from Arsenal and how restrictive that was, so they already have that to contend with.”
Meanwhile he had praise for manager Mauricio Pochettino, in particular the way he has succeeded in getting a crop of English players to excel.
“Look at the way he’s nurtured the players, we’re looking at Kyle Walker playing out of his skin, Danny Rose," he added.
"The performances of some of these players, Dier, we’ve a lot to be grateful for."
Spurs are in action on Sunday at home to Stoke City and victory would send them three points clear of Arsenal in the Premier League table.