Tottenham were set to finish second this season, but they ended up third after losing 5-1 to Newcastle United at St. James’ Park on Sunday afternoon.
Spurs’ bitter North London rivals Arsenal finished second, and many of their fans have been revelling in this success.
Chelsea, who won the Premier League title in the 2014-15 campaign, themselves have had a torrid season and finished as low as 10th in the standings.
Arsenal legend Wright believes that fans of Arsenal and Chelsea taking the mickey out of Tottenham is actually a compliment to Mauricio Pochettino's side.
The former England international has also advised Spurs to take inspiration from Team Europe’s narrow defeat in the 1983 Ryder Cup.
“The way Chelsea and Arsenal fans are celebrating Spurs not winning the league signifies the change in Tottenham,” Wright wrote in The Sun.
“It’s like the Ryder Cup. America used to hammer us all the time. Then in 1983 Seve Ballesteros was asked back, they beat us by a point and everyone was disappointed.
“But Seve said: ‘They always beat us but look at how happy they are to beat us this time. We are emerging now.’
“That’s how Tottenham should look at it. Chelsea and Arsenal, two teams that are supposed to be in a different stratosphere, are now bricking it because Tottenham are coming.”
Tottenham finishing below Arsenal and Chelsea has been the norm for quite a while now, but things could change in the coming years.
Spurs were genuinely brilliant throughout the 2015-16 campaign and were in the running for the league title until the final weeks.