The Foxes came from 2-0 down to earn the point on Sunday with two late goals.
Van Nistelrooy said afterwards: "It’s massive, it’s vital.
"I emphasised it last week when I walked in Seagrave and had my first meeting with the team. I can’t believe it’s only been one week actually!
"This squad has to do well to stay in the Premier League, there’s no other way. 11 starters, we need 5 subs to be contributing. I demand a lot from the wingers, off the ball and on the ball. I demand a lot from the full-backs and strikers. I’m glad we have a lot of options that we can put on in the squad and I’ve used them all in the two games."
On Vardy's equaliser, he said: “That was a brilliant moment.
“So late in the game, the 91st minute, when you have the calmness and the composure to decide on these things, that’s absolutely top class and we’re happy we have that in our team.
“If you don’t pass, you have to score. He made sure we were going to get that equaliser. I think he felt we deserved that. If I would have passed it? I don’t know, I’ll have to look back at the goal.
“But the performance of the whole team put him in position. If I relive the second goal, where we were pressing high, we won the duel, and played forward from there, and we went for goal from the turnover. That’s where the ball ended up with Jamie.
“I liked that. I enjoyed that, the whole sequence. That’s why, as a team, we put him in the position there, and that’s where we want to put players who can make the difference for us.”
He added: “We were realistic after the West Ham game. We were very effective in scoring three goals but we let West Ham in way too much. We acknowledged it. Today the performance was way better than Tuesday, in that sense.
“We controlled the game and put a lot of pressure on Brighton, who are one of the best footballing sides in this league. That’s a compliment to the team.
“We didn’t give a lot of chances away and scored another two goals. We got only one point today, with a better performance than Tuesday, but it’s a silly old game, isn’t it?”
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