The result leaves Leicester 12 points away from 17th place and Premier League safety.
After the 2-0 defeat, Van Nistelrooy admitted: “We live in reality.
“We know what the situation is, 12 points with eight games to play. Mathematically it’s not over and we have a responsibility to keep going and there’s no other way than doing that.
“It’s personal pride and honour by doing the job as good as you can, that is my drive. That’s why I get up every morning.
“That demands character, resilience in dealing with the situation you’re in, looking in the mirror and going back to the players and staff and do better, and get the best out of people around you. That is how I try to do it.”
On the result last night, Van Nistelrooy rued City's early goals scored by Jack Grealish and Omar Marmoush.
“The form that we’re in and the sequence of games we’re in, if you start like this, it makes it extra hard,” van Nistelrooy said.
“The boys had come in with positives after a good break, after a good couple of weeks of training. Away at Man City you want to have a good start and get through the first 15 minutes.
“But with the ball lost in midfield and with the communication between keeper and centre-back for the second and before the half-hour we’re 2-0 down and it’s going to be a long night.
“They were looking for more goals so we had to really fight to go in with a 2-0 result at half-time. That made it very difficult for us.”