The Foxes squeezed past the League Two Hatters on penalties in August, with Daniel Iversen saving three spot-kicks.
They host Newport on Tuesday aiming to reach the last 16 and manager Rodgers will resist the temptation to rotate.
“We want to get through, I won’t be making too many changes,” he said. “We have a game on Tuesday and a lot of the players need to be ready to go again.
“I changed the team about when we went to Stockport and we nearly went out. I don’t want to do that. I want to go through. I’ve shown that every time I’ve been here in the cup competitions.
“We’ll make some changes, naturally, but there won’t be too many.”
The Foxes climbed to 14th in the Premier League following victory at Goodison Park, after goals from Youri Tielemans and Harvey Barnes.
Tielemans, out of contract in the summer, was captain again in the absence of Evans, and Rodgers has been impressed with his attitude.
He said: “He doesn’t need the armband to play to that level, but he’s a player of great maturity. Even though he’s in the last year of his contract, how he looks after himself and drives the other players on is fantastic.
“I know he is really enjoying the responsibility.”
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