The goalkeeper, son of United legend Peter, has kept 15 clean sheets this season as the Foxes stunned the football world to win the Premier League.
He is the same age as his father when Schmeichel senior won the first of his five titles at Old Trafford, 29, with United dominating the 1990s.
And Schmeichel junior admitted he dreamt of following his father and winning titles himself.
“That is the just the beauty of football. Anything can happen,” said the Denmark international.
“You play football for these type of moments and that is what you dream of as a kid. This is a dream come true definitely. The trophy is a massive experience and it is all a bit of a blur.
“It is an amazing achievement, everyone is buzzing as you can see and we still haven’t taken it in.
“It is a massive moment, there is no question, and something the whole city can be proud of.
“Claudio (Ranieri) has come in and inherited a well- assembled squad that Nigel Pearson had created with a good team atmosphere. He has built on that and tweaked it and put his own little stamp on it.”
Dad Peter was at the King Power Stadium on Saturday to see Leicester beat Everton 3-1 and then lift the league trophy, and Schmeichel junior insisted family are important to him.
“The family are the people who see you day in day out through all the bad times as well,” he added. “People see you for 90 minutes a week, they don’t see the all the effort and time that goes into the weekend. They obviously have to make a lot of sacrifices time-wise and it is nice to be able to share it with the entire family.”
Leicester go to Chelsea for Sunday’s season-finale before their trophy parade on Monday through the city.
Meanwhile Liverpool goalkeeper Simon Mignolet believes the club can take a lot from a battling draw with Chelsea as they look ahead to next week’s Europa League final. Christian Benteke scored a last-gasp equaliser as the Reds snatched a 1-1 draw against the Londoners in a relatively unimportant Barclays Premier League clash at Anfield on Wednesday.
Goalkeeper Mignolet thinks lessons can be learned after Liverpool let their intensity drop following a bright start and confidence can be gained from how they fought back.
Liverpool have just one more game, Sunday’s trip to West Brom, before attention can fully switch to next Wednesday’s clash with Sevilla in Basle.
Mignolet said: “You just want to go into the final with confidence and the only way to do that is by putting in performances.
“I think the biggest message this shows is that if you don’t start well, or play how we played in the first half, we can get into trouble.
“That is maybe the best message we could have and take forward. We have to be 100 per cent focused and ready, play like we played the last minutes and first minutes of the game - not the last 15 minutes of the first half.
“But we never give up - something the gaffer always talks about. It doesn’t look like any coincidence any more, that we score in the late stages. We have to keep that going. We have to show that mentality to never be beaten.”