Sturridge, a £12million signing from Chelsea earlier this month, became the first Liverpool player since Ray Kennedy in 1974 to score in his first three matches before Steven Gerrard and a Ryan Bennett own goal completed the rout.
"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% 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.
"We had real fluidity with our play at the top end of the field. Daniel has pace and power but he is also clever and that was important today as Norwich are tough to break down and a tough team to play against. The second goal was a wonderful demonstration of how good players can link together.
"It was great vision by Daniel to see the run of Luis coming from the outside, great weight of pass by Lucas, and Suarez found himself one versus one. I've seen it in training in the early part he has been here.
"Behind that you have Steven Gerrard, who in that form I think he used every club in his bag.
"His passing was phenomenal and the goal he scored was trademark Steven Gerrard."