Starting the last round of fixtures in fifth place, the Foxes knew that their best hope of finishing in the top four was a win, while hoping that Liverpool and Chelsea slipped up in their respective final games.
Chelsea did leave the door open, losing 2-1 at Aston Villa, but Leicester were unable to do their part, falling to defeat at the King Power Stadium despite leading twice to finish a point behind Thomas Tuchel’s Blues.
It was Bale who hammered in the final nails, finishing low into the bottom corner to put Spurs ahead in the game for the first time in the 87th minute, before following up his own shot that had hit the post to add a second in added time.
In truth, though, it was on own goal from Kasper Schmeichel that really ripped the heart out of City’s challenge, with the keeper punching a corner into his own net under pressure to make the score 2-2 with 14 minutes left.
Prior to that, with Chelsea losing at Villa, two coolly taken penalties from Jamie Vardy – both of which he was fouled for – looked to be sending the Foxes into Europe’s premier competition for just the second time.
The match may also represent the final one in a Tottenham shirt for talismanic striker Harry Kane, who has signalled his desire to leave the club this summer.
If so, the England captain has signed off with the 221st goal of his Spurs career – a fine first equaliser from inside the box that also takes him to a Golden Boot-winning tally of 23 for this league campaign.