The Foxes scored took the lead inside 21 minutes through Nigeria international Kelechi Iheanacho before he got his second two minutes after the break with a 25-yard drive which took a ricochet off Bruno Viana.
Dennis Praet got Leicester’s third midway through the game before James Maddison capped a man-of-the-match performance with a goal on the 78th minute mark.
Speaking to the media after the game, Rodgers was delighted with the players’ performance after altering the starting lineup, and was quick to laud Iheanacho for his blistering display.
“We had to work for it. By the end, we were very good, it was a tight first half, with a couple of things to put right in terms of our defending. But second half, after we got the goal we were very dynamic, very strong. We created a number of chances, and it ended up as a great victory for us,” the former Liverpool and Celtic boss told Sky Sports.
"He's (Iheanacho) a boy who I see every day in training, I know when I put him in he gives his all. His first goal was fantastic, he's scored another one, created the third for Dennis. He's always ready, he knows Jamie Vardy's one of the best strikers in the world, but he plays a wonderful part in ensuring we continue with our momentum and I thought he was excellent."
Next up for Leicester City is a game against Wolverhampton Wanderers in the Premier League on Sunday.