Spurs finished the campaign with an enthralling 5-4 victory over Leicester City in their last game at Wembley ahead of moving to their new stadium on the site of their old White Hart Lane ground, Erik Lamela and Harry Kane each scoring twice in a pulsating end-of-season fixture.
However, a second-half collapse, conceding four goals in 27 minutes to lose 5-4, left them with only one win from their final seven games in the league.
But Erik Lamela scored twice either side of having the shot that a luckless Christian Fuchs diverted into his own goal, before Harry Kane netted the victor after Vardy's second had levelled the score at 4-4.
Spurs booked a third successive year in Europe's elite club competition, in a season where they played "home games" at Wembley and all the other teams around them spent massively. "We had to manage things better after our third goal".More news: Celtics open East finals by ripping Cavaliers
Lamela inspired the fightback by twice finishing from Kyle Walker-Peters assists, and it was the Argentine's strike that forced an own goal from Christian Fuchs to put Spurs in front by the hour mark. Lloris produced another fine save to deny Iheanacho and the 2016 champions leveled in the 73rd when Vardy got in behind the defense and smashed high into the roof of the net from an acute angle.
Spurs were caught cold in just the fourth minute when Vardy was allowed a free run to glance a header from Mahrez's teasing left-wing free-kick into the far corner.
Leicester's lead was at two for just two minutes.
After a poor header from Eric Dier, Iheanacho picked the ball up, shrugged off Wanyama's challenge and launched an unstoppable effort from 25 yards that rifled into the top corner.More news: Bombings claim 13 in Indonesia
Leicester and Tottenham contributed to a game which matched the all-time record for goals scored in a single match at Wembley, in a topsy-turvy game which did not appear to have little meaning for either side.
It was his 40th goal of the season, the most by a Spurs player since Clive Allen bagged 49 in the mid-1980s.
"It's insane to lose a game where you've scored four goals away", Puel added.More news: Britons kidnapped in DR Congo gorilla sanctuary 'relieved' to be released