Boss Brendan Rodgers urged Leicester to create history after the Foxes reached the FA Cup semi-finals for the first time since 1982.
Kelechi Iheanacho's double and Youri Tielemans' strike beat Manchester United 3-1 to set up a last four clash with Southampton at Wembley next month.
Mason Greenwood did equalise in the first half but United were second best as their hopes of winning a 13th FA Cup ended.
Leicester have reached the final four times but never won the competition and Rodgers wants to end that run.
"We are in the semi-final and we have a chance to get to the final and create history," he said after only the Foxes' second win over United in 23 years. "When it comes we will fight and give everything we can to achieve that.
"For the club to get to the final and win the trophy would be really special. It's a trophy in their history they haven't won. I would be so happy for the owners.
"There are lots of teams ahead of us in terms of budget or whatever else, maybe history, but the ambition is there to win titles and be competitive.
"It's a tough game in the semi-final but the club has never won the FA Cup so to be able to do something like that will be special.
"We were very complete. You are playing against a top-class team but it was an outstanding performance against a very good side.
"We have developed very well, the confidence comes when you start to win big games against big opponents. We passed the test. It was a measure of how well the players are progressing."
Fred's howler gave the Foxes a 24th minute opener when his backpass to goalkeeper Dean Henderson was short and Iheanacho stole in to score.
Greenwood levelled 14 minutes later when he swept in Paul Pogba's cross but that is as good as it got for United.
Tielemans restored Leicester's lead seven minutes into the second half when he held off Fred's half-hearted challenge and drilled into the bottom corner.
Jamie Vardy shot wide with just Henderson to beat but Iheanacho sealed the tie when he escaped from Scott McTominay to head in Marc Albrighton's free-kick with 12 minutes left.
It was United's first domestic away defeat in 30 games but they were well beaten with Leicester rarely needing to hit top gear.
The Europa League is now their only realistic chance of a trophy and boss Ole Gunnar Solskjaer, who made five changes from Thursday's win at AC Milan, had no regrets over his team selection having left talisman Bruno Fernandes on the bench until the second half.
He said: "I would have started the same team again. Every team selection has reasons behind it. On Thursday Bruno broke all his records physically and the boy is not inhuman.
"He has played a game every three or four days. It was a chance to start both Donny (Van de Beek) and Paul (Pogba) but the accumulation of games maybe caught up with us.
"We knew we had substitutes who could come on and make a difference Everyone could see we weren't as sharp as we have been.
"You are always disappointed, especially when it's the end of the line of a cup run. We couldn't find the normal spark, brightness and energy.
"Maybe all the games caught up with us. Thursday was a big night and today we didn't have the zip."
