The Brewers beat City 4-2 in August in the Capital One Cup but were never in the hunt in this third-round tie with first-half goals from Chris Wood and Ritchie De Laet giving the Foxes a 2-0 win.
"It wasn't the greatest start to concede a goal after three minutes," said Rowett. "In the week we had worked on having a very solid base because we know the sort of side Leicester are.
"They are going to come at you, and at home they are a terrific side.Their home form is sensational this season.
"So it was important that we weathered that early storm, so to concede after only three minutes leaves you with an absolute mountain to climb.
"But you can't go stupidly forward because you then risk conceding two or three more goals. But when the second goal went in it makes it that much harder.
"To hope to do it twice at Leicester was always going to be difficult. You look at Leicester's team and think they could get five or six if you go at them. They are a terrific side and I hope they can get up into the Premier League."
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- Ritchie De Laet