The result, which matches Manchester United's 9-0 win against Ipswich in 1995, was only confirmed in stoppage time thanks to Jamie Vardy's penalty.
Both Vardy and Ayoze Perez scored hat-tricks, with the visitors' task aided by Ryan Bertrand's red card for a reckless challenge on Perez in the build-up to Ben Chilwell's opener.
That opened the floodgates for Leicester, who turned on the style just two days before the first anniversary of the helicopter crash that killed the club's former chairman Vichai Srivaddhanaprabha and four other people.
Rodgers said: "I'm very pleased to see our work rate, we scored some great goals and we were very hungry tonight.
"It was horrible weather but our focus was outstanding. I'm very pleased how we defended, and we were ruthless. I'm very proud to stand and be the manager of that team.
"We wanted to get the ball back quickly and attack again. A mark of the good sides is you don't let up. We wanted to show we're a good side and we certainly did that in the second half.
"We were ruthlessly simple in our game. When you're so many goals up you can easily slow but we kept focused. We want to be a top team and to be a top team you must be clinical.
"It was a very good team performance and we're pleased to keep a clean sheet. It's good for our goals for but the clean sheet is equally important.
"We believe in our work. The players are finding confidence and that bodes well going forwards."