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Harry Kane (R) scored on what could be his last game for Tottenham to deny Leicester a place in the Champions League
Brendan Rodgers said he had "nothing but admiration" for his Leicester players despite the devastating 4-2 defeat against Tottenham that denied them a place in the Champions League on Sunday.
Jamie Vardy twice put Rodgers' men ahead from the penalty spot, leaving them on course to reach the Champions League for just the second time.
But Harry Kane scored on what could be his final appearance for Spurs before Kasper Schmeichel's own goal and a late double from Gareth Bale denied Leicester.
The Foxes' late collapse meant Chelsea, beaten 2-1 at Aston Villa, pipped them to a fourth place finish in the Premier League by just one point.
Tottenham secured seventh place and a spot in next season's Europa Conference League.
Leicester spent more days in the top four than any other club this season, but for the second consecutive year they fell away in the final weeks of the campaign to miss out on the riches and prestige of Champions League football.
"It's hugely disappointing for us. We fought so hard all season. I always said you're judged after 38 games and unfortunately we couldn’t quite make it," Rodgers said.
"I have nothing but pride and admiration for the players. They've constantly had things go against them with injuries.
"If you look at the importance of the players out today, we were able to take it down to the last game and the last 15 minutes."
Rodgers refused to condemn his players for failing to finish the job, pointing to their FA Cup final triumph last weekend as proof of their progress in his reign.
"When we started work together we were mid-table and just over two years later we're challenging the elite and won the FA Cup for the first time in our history and we're on the right path without the resources of other teams," Rodgers said.
"I have nothing but pride. The ownership have given me amazing support. The players have given me their heart and souls every day.
"I'm so disappointed for them we couldn't get over the line."
For much of a thrilling afternoon, it looked like the FA Cup winners would do just that as Vardy slotted home his first penalty on 18 minutes.
Kane is keen to move on from his boyhood club after Tottenham also missed out on the Champions League for a second straight year.
But the England captain secured the consolation prize of winning the Golden Boot as he slammed home his 23rd Premier League goal of the campaign four minutes before half-time.
Vardy was spot on again seven minutes into the second-half to put Leicester back in pole position to round off a fine season after lifting the FA Cup for the first time in their history last weekend.
Schmeichel was one of the heroes at Wembley eight days ago, but the Dane's mistake cost his side dear with a place in the Champions League worth at least £60 million.
The Leicester captain flapped at a corner to punch the ball into his own net 14 minutes from time.
With the home side then chasing a winner, Bale struck twice in the final 10 minutes to also sign off his loan spell from Real Madrid on a high.
Leicester were furious Kane was not penalised for handball before he teed up the Welshman to slot into an unguarded goal.
Bale then tapped home his 16th goal of the season after his initial effort came off the post deep into stoppage time.
Asked about his future after the final whistle, Bale gave an intriguing answer.
"It just has to happen after the Euros," the Wales attacker told Sky Sports.
"I know what I'm doing but it'll just cause chaos if I say anything now."
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