The Foxes lost star striker Jamie Vardy to injury on the stroke of half-time at a point when they only had a one-goal lead, courtesy of Harvey Barnes’ 23rd-minute tap-in, to show for their sheer dominance.
But Ricardo doubled the Foxes’ advantage with a sumptuous strike in added time, and although Hammers skipper Mark Noble pulled one back from the penalty spot early in the second half, City deservedly wrapped up the points with an Ayoze Perez brace in the final 10 minutes.
Confirming Vardy only sustained a glute injury, rather than a hamstring problem, Rodgers said: “He’s a fantastic player, and very, very important for us, but you are never going to succeed or do well if you just rely totally on one player.
“Of course, when you have a player of his quality, he is always going to be a miss, so it’s particularly important to have players who can come into a game and you don’t change so much of your rhythm.
“Kelechi (Iheanacho) came in and he was very, very good. He wants to run in behind, he was powerful, his touch was good, he works ever so hard, and he always looks like he can create and score goals. I thought he came in and did very well.
“Overall, I thought the performance was very, very good. From the first whistle we played with a high tempo, the speed in our game was good, the creativity was good. We thoroughly deserved it, so really pleased.”
It is highly unlikely Rodgers would have picked Vardy for this weekend’s FA Cup fourth-round tie at Brentford, but it remains to be seen if he will be fit in time for next Tuesday’s second leg of a Carabao Cup semi-final at Aston Villa.
Rodgers added: “It wasn’t his hamstring, so that’s good news for us.
“He just felt a twinge in his glute, so we will wait and see on that one in the next day or so, but thankfully his hamstring is fine, and we’ll assess things over the next couple of days.”
Midfielder Nampalys Mendy will also be assessed after limping off just after the half-hour mark with a knee injury.
For United boss David Moyes there were no complaints as his team were distinctly second best throughout, with only goal difference now separating the Hammers from a place in the bottom three.
Moyes said: “I’m extremely disappointed.
“The first half was really poor. I was hoping to have scraped through to half-time at 1-0 and then done something about it.
“We did improve, we rallied and the introduction of Michail Antonio (at the interval) helped us.
“But we have to be honest, Leicester City were far better, played better, and they deserved it, we didn’t, on that performance.”