The Foxes took the lead twice during the game through two Jamie Vardy penalties however they were pegged back by golden boot winner Harry Kane and a Kasper Schmeichel own goal.
Gareth Bale then came off the bench to score a brace and consign Brendan Rodgers' side to Europa League football for next year.
Foxes fail to take advantage of fortunes elsewhere
Heading into the fixture, Leicester's top four destiny was out of their hands, with the Foxes relying on both Chelsea and Liverpool to slip up if they were to qualify for the Champions League for the second time in the club's history.
Whilst the latter secured a routine win against Crystal Palace, Chelsea offered the East Midlanders a lifeline having been beaten by Aston Villa.
With 15 minutes to go and both Leicester leading and Chelsea struggling to find an equaliser at Villa Park, it seemed as if fate would be on the Foxes' side however they couldn't live up to the pressure, instead conceding three goals and losing the crunch fixture.
It's not the only time Leicester have struggled to cope with the pressure and this one result alone is not the sole reason they missed out on a top-four spot.
With nine defeats on home soil this season and points dropped in games where they were arguably favourites, the Foxes know where there is significant improvement to be made. In the past two seasons, nobody has spent more days (242) in the top four than Leicester City yet when it mattered most, they haven't finished in those positions.
Injuries and squad depth hit Leicester hard
As Wesley Fofana left the pitch in tears having suffered an injury that prevented him from continuing in the first half, there was an overwhelming sense of Groundhog Day at the King Power Stadium.
With a lack of defensive options due to other injuries and Rodgers seemingly not willing to trust Daniel Amartey or give Wes Morgan one last chance to be a hero, he opted to bring on Nampalys Mendy and drop Wilfred Ndidi to centre-back - exactly as he did right at the beginning of the campaign.
Whilst Mendy is capable of doing a job, it's hard to argue just how much the Foxes missed Ndidi's presence in the middle of the park. Injuries have been a common occurrence for Leicester far too often this year too.
The likes of James Justin and Harvey Barnes have all been missed at the crucial end of season run-in and other key players such as Ricardo Pereira, James Maddison, Caglar Soyuncu and others have all been injured for significant periods at different points of the year.
Even though this could be classed as unlucky in some respects, there is also a growing feeling that the depth of quality needs to be improved if Leicester really want to remain fighting with the elite.
On paper, the starting XI is as strong as many others in the league, but when you look to the bench of the Foxes, there are few stand-out candidates that you feel can change the game when needed.
The return of Kiernan Dewsbury-Hall into the first-team fold will be timely boost however and with plans to strengthen the squad in the summer - most notably the reported acquisition of recent Ligue 1 title-winning midfielder Boubakary Soumare from Lille - it seems steps are already being taken to ensure they can sustain a challenge on all fronts in the future.
Plenty of reasons to be positive
When the full-time whistle was blown in the East Midlands on Sunday there was once again a feeling of disappointment. Disappointment that for the second year running, Leicester had thrown away a place in the ring with Europe's elite.
The feeling of frustration was understandable, but at the same time, there was also a reflection of just how far they had come. As the players walked around the pitch in their lap of appreciation in front of 8000 Foxes, on display with them was their greatest achievement - the FA Cup trophy.
The feeling then turned from disappointment to pride and memory of just how special that day at Wembley Stadium had been for both players and supporters. In 10 years time, those fans won't remember finishing fifth, but they will remember securing the trophy that had eluded the club for its entire 137-year history for the rest of their lifetimes.
Not only that, Leicester were also able to record their second highest points tally in the Premier League and also qualify for Europe for the second consecutive season for the first time ever. A remarkable achievement for a side that just six years ago were celebrating survival in the top flight.
Under Brendan Rodgers there is a clear plan. Any worries of him leaving for another job were cast aside when he reaffirmed his commitment to the club in his post-match press conference. Next season will be all about doing the same. Challenging for the European spots, competing in the cups, and giving it their all in Europe is the hope and next time, they will hope they can finish the job.