A brace from striker Chris Brown at Deepdale on Tuesday made it five wins and one draw from North End's six matches so far and it is a better beginning to the season than Irvine could have hoped for.
"I would have taken this start if it had been offered to me beforehand," the Scot said.
"If we can get through the next game at Ipswich and still be unbeaten, it will be a very satisfactory start."
Irvine was delighted to see his homework on the Foxes pay off.
He said: "Everybody knows now that I went to Macclesfield and saw Leicester and I was really impressed with them. I have watched a couple of games on DVD and I think they are a very well organised team, very hard-working and they have some quality and momentum on their side.
"They only lost four games in the league all last season so are used to winning. They are playing with a great deal of confidence and self-belief and so we knew it would be a very difficult game.
"We got off to a terrible start. We gave the ball away very cheaply and were punished. We then rallied, showed a lot of character and started to play better football.
"I said to the lads at half-time I felt the team that was best at getting the ball back in the second half would win. We did that a lot better in the second half."
Leicester manager Nigel Pearson could not hide his disappointment at not going through to the next round, with Nicky Adams netting the Foxes' goal.
He said: "It was a decent game, both sides had chances but it's disappointing to lose.
"I gave a few players a good opportunity to get a game tonight. There were some good performances out there.
"We were a bit unlucky with the equaliser, it took a deflection but that's how it happens I'm afraid sometimes. Their second goal was disappointing.
"The most important thing for us was the fact we wanted to go through. We didn't quite manage that but we look forward to the next game now."
Leicester started with early domination and took a seventh-minute lead when Dany N'Guessan's neat pass was met by an Adams chip from 12 yards out.
But Preston fought back from being behind and pulled level eight minutes later.
Eddie Nolan's cross saw Brown produce a right-footed shot that took a slight deflection on the way in.
Nolan also laid on Brown's winner, putting in the 65th-minute cross which he headed home to send North End through.