Jordan Ayew had Leicester ahead before the Reds stormed back through Cody Gakpo, Curtis Jones and Mohamed Salah.
Van Nistelrooy said: "We know when you come here you want the start that we wanted.
"We knew we had to be compact and defend well. Which we did and we had a couple of breaks. We were in the game for a long time and at 2-1 we had the Daka chance - these are moments.
"In these games you have got to take them.
"When you are 1-0 up and we had a break with Stephy Mavididi on the break which led to a goal kick.
"A quick take from Allison and they combined into Gakpo. Him coming onto his right foot can be dangerous."
On Jakub Stolarczyk's debut he said: "Well done for Jakub coming in. He come back from a long injury, he recently played in the under-21s and he had a great game.
"It is up to us to keep developing and creating gameplans for every opponent.
"The gameplan was there, players knew what to do and acted too it, but today was the maximum possible.
"Anfield is not the place where we usually collect the points, but for our development we have to do it as the points need to be collected."