Leicester captain Kasper Schmeichel said his joy at leading the Foxes to a first-ever FA Cup was indescribable after beating Chelsea 1-0 at Wembley.
Youri Tielemans' 25-yard strike gave them victory, although they needed the video assistant referee to rule out a late Wes Morgan own goal.
Denmark goalkeeper Schmeichel made superb saves to prevent Ben Chilwell and Mason Mount putting Chelsea level.
"I'm so happy I can't begin to describe it," Schmeichel told BBC Sport.
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"To think of the people who have lifted this trophy, and to be able to do it today is beyond my wildest dreams."
More than 20,000 supporters attended the final as Leicester finally won the FA Cup, having been runners-up on four previous occasions.
"It's an amazing feeling," Leicester boss Brendan Rodgers told BBC Sport.
"I'm very proud, it's a historic day for the club. Winning the FA Cup for the first time is clearly a special day.
"I wasn't aware before I came to Leicester that they'd never won the FA Cup, that they had lost in four finals previously, so to be able to give that to the owners and the fans is so special."
'An old-school Cup final-winning goal'
Leicester's victory was built on four moments that will live long in the memory – Belgium midfielder Tielemans' unstoppable long-range strike, Schmeichel's two world-class stops and VAR's marginal offside call against former Foxes full-back Chilwell that denied Chelsea a late leveller.
"Youri Tielemans' goal was like an old-school FA Cup-winning goal, but also Kasper Schmeichel's saves – those are the special moments you need in games," added Rodgers.
"Overall we were the better team, super aggressive, pressed well. We were always a threat with the ball.
"Chelsea are an amazing team, that's why they're in a Champions League final, but I thought we deserved it.
"The reality is there are other teams that can provide budgets way beyond us at Leicester City. We have shown we can compete and fight against it."
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It was a fourth FA Cup triumph for the Schmeichel family, with Kasper's father Peter having won the trophy three times with Manchester United during the 1990s.
The Foxes keeper, a key player in their 2016 Premier League win, added: "It's what dreams are made of, I've dreamed about this since I was a child.
"It was horrible [the last few minutes] – I was begging for the final whistle. But now it is all worth it."
'His family have built this club towards glory'
A popular figure among Leicester's celebrations was Foxes owner Aiyawatt 'Top' Srivaddhanaprabha, who took over the running of the club after his father Vichai died in a helicopter crash in 2018.
The Thai family has brought Leicester scarcely believable success since purchasing the club in 2010, with the Foxes now adding the elusive FA Cup to that unlikely Premier League triumph five years ago.
"It's emotional for Top and his family because they have built this club towards glory after winning the Premier League, and now to win the FA Cup is amazing," said match-winner Tielemans.
"We will give everything for this club and for those men that built this club and built this history and legacy."
Manager Rodgers added: "I'm so pleased for Khun Top and the family. It was a dream of theirs to win the FA Cup and we have been able to deliver that."
Schmeichel said the Leicester players had a special way of paying tribute to their former owner Vichai, revealing: "We have a picture on the inside of our shirts so he's always with us.
"I'm so proud of everybody. Everybody contributed to get to the final, everyone has played and been sensational. Everyone behind the scenes, all the team behind the team, the medical staff and everyone.
"When you work together and do things properly and you have an internal belief, that's what we can achieve."
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Leicester will face the same opposition in the Premier League on Tuesday night, knowing victory at Stamford Bridge will ensure a second shot at the Champions League, a competition they reached the quarter-finals of in 2017.
"Today we enjoy it but we can't for too long because they are a top-class side and they will want revenge," added Schmeichel.
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