Emile Smith Rowe and Adama Traore struck for the Cottagers on the day.
Van Nistelrooy later said: "No, I don't agree. I thought today was extremely disappointing because it wasn’t good enough in all aspects of the game.
"I saw more (on) Wednesday than today. Of course, results hurt and are disappointing, but today, a lot more because we lacked in too many areas that influence a football match.
“For me, it’s about today. The disappointment is big because we lacked in all aspects of the game. In the other games that I’ve managed, today is the most disappointing one for me.”
He also said: “We have to deal with it. We cannot change it. We have to face it. Don’t feel sorry for anybody.
"We are professionals and we have to deal with it. We have to make sure that we perform so the crowd is up and supportive. That’s our task. There’s no other excuse or explanation necessary. It’s up to us and sometimes you deserve criticism and you have to accept it because it wasn’t good enough and do better next time.
“We cannot change it. In the moment, if something happens like that, it’s only a sign, for us as a team, to stick together more than ever. That is the key to survive.”