City held off a dramatic fightback to move six points clear at the top of the Premier League with a breathless victory at the Etihad Stadium, with this game swinging from one side to the next before City sealed the win.
The free-scoring champions raced into a 4-0 lead inside 25 minutes at the Etihad Stadium but the visitors fought back to 4-3 in a Boxing Day classic at the Etihad Stadium.
It took a further goal from Aymeric Laporte and a late effort from Raheem Sterling, his second of the game, to finally kill off the Foxes’ unlikely comeback.
Sterling had been on target from one of two penalties awarded to the hosts in the first half, with former Leicester star Riyad Mahrez scoring the other. Kevin De Bruyne had opened the scoring, with Ilkay Gundogan also getting on the scoresheet.
Leicester’s replies came from the impressive James Maddison, Ademola Lookman and Kelechi Iheanacho early in the second half, but the injury-hit visitors ultimately could not maintain the momentum.
Yet it was of great credit to the Foxes that they managed to make the game such a contest.
"The situation we’ve been in the last 10 days, we played Manchester City with one of the very few weeks they didn't have a midweek games," said Rodgers.
"We are clearly short of players. We’re not getting the violins out. You see what we’re missing. The players aren’t available. The players that are will give everything.
"Clearly we didn’t make a great start. You expect to be up against it. The second goal was nowhere near a penalty. It's so frustrating.
"At half-time we said to the players can we win the second half, can we get closer to them? The biggest factor was it was so important not to unravel physically and mentally.
"They’ve never done that. At 4-0 away, with everyone going against us, it could have been easy for the players to do that. But they didn’t.
"At 4-3 we’re disappointed with set-pieces. We had two big chances at 5-3. The second half was so encouraging. We’re not overly pleased at losing the game."
Pep Guardiola admitted his side were rattled by Leicester, as his side moved six points clear at the top of the table.
"It was weird. Even at 4-0 in the first half, every time they had the ball they arrived in the final third delivering good passes," said City boss Pep Guardiola. "They moved a lot of players. They have a lot of quality. They are a master of counter-attacks.
"They changed in the second half. The way they played they didn’t play to press high. They were close. The game was so dangerous.
"We didn’t play bad in the second half. Ruben Dias was not aggressive because he was one yellow card away from being suspended so he was more cautious. The game was not over. With set-pieces we could win the game."