Suarez took his tally to 20 for the season with the Reds' second, while Sturridge, a £12m signing from Chelsea earlier this month, became the first Liverpool player since Ray Kennedy in 1974 to score in his first three matches.
"I couldn't have asked for more. The players were brilliant in their application and their game and it was a great performance," said Rodgers.
"They (Suarez and Sturridge) linked very well, obviously both got on the scoresheet, which was great.
"Luis has done what he has done for us all season, given us 100 per cent every game, and he combined well with Daniel up front.
"I think it gives the opponent someone else to worry about. Suarez has been incredible for us but you now have a recognised goalscorer up beside him.
"Daniel has pace and power but he is also clever and that was important as Norwich are tough to break down.
"The second goal was a wonderful demonstration of how good players can link together.
"I thought defensively we were also very intense and aggressive in getting the ball back. It was a terrific performance."
Rodgers revealed Jose Reina, who missed the match because of a thigh injury, had an operation to repair a nose broken at Old Trafford last week.
"Pepe was injured and Brad Jones came in and kept a clean sheet," he added.
"He had a thigh problem before the game last week and he played and the assessment afterwards was it had got worse - plus he had broken his nose.
"He had an operation to fix the nose yesterday so we will see how he is by next week and review it from there."