Swiss defender Bruno Berner scored a late consolation for the hosts but it was not enough to prevent Nigel Pearson's side slipping to their first league defeat at the Walkers Stadium in 25 outings since losing 1-0 to Millwall on September 13 last year.
Irvine said: "We spoke about their record a lot leading up to the game, but I felt it was possible to come here and win if we played well, and we played well.
"It was an incredible record, absolutely amazing. One of the big things I was stressing to the lads at half-time was that you don't get that kind of record without coming back.
"There must be a number of times that Leicester have been behind at half-time and come back and we were very mindful of that.
"We knew we would have to be extremely well organised and very disciplined when we didn't have the ball in the second half and be able to use it well when we did have it, and I think we did that."
The Scot added: "We were very good for the majority of the game. We put ourselves under a bit of pressure through not defending properly in the 90th minute, but apart from that I thought it was an excellent performance.
"There were a lot of good performances. Looking around the team it's hard to pick anybody who didn't play well.
"We created a lot of chances, Mellor scored one and made one and should have another one but took a bit too long on it.
"Our defenders had to play well in order to make sure we didn't get caught out because their strikers are a real threat.
"Matty Fryatt is a good player. His movement is good and he runs across the line well and times his runs behind well, and Steve Howard is a real presence in the air so we had to be good to make sure we didn't get caught out."
Pearson had no complaints after seeing Leicester lose their proud unbeaten home record, and the City manager expects his side to quickly bounce back from the disappointment.
"I think we were beaten by a better side, simple as that," said Pearson. "They were worth their win even though we created a lot of chances.
"We had a very good run at home but it doesn't make it any easier to take. But we will take it on the chin and dust ourselves down and get ready for the next game.
"There are some disappointing aspects for both their goals, but they showed what they are and that's a very accomplished side.
"I've got no complaints. It's disappointing but they were very disciplined and scored a very good second goal on the counter attack, which we obviously aren't happy about. But that's life."