Bruno Fernandes, Alejandro Garnacho and an own goal saw United to victory over Sunday.
Caretaker manager Van Nistelrooy, in his last game in charge, said: "It was professional, you could see that players were fighting through the game. We scored two great goals and there were some good bits but we didn't have real control of the game.
"It was an important three points. In the four games Bruno scored some important goals, assisting too so he is back producing. That's the Bruno that is helping the team the most.
"I spoke to Alejandro Garnacho before the game, he has played a lot of minutes and I wanted him to make an impact off the bench and I'm glad it worked out. We said 'let's make the most of these four games', get the maximum out of it and I think we did an OK job.
"I really enjoyed it, it's been a short but amazing period. We are in an uncertain position but we tried to do our jobs and help the club which is important.
"There are a lot of feelings there, the way the fans supported me and the team always in difficult moments it was a special moment. To close down this block of games with good results and a good connection I can't thank them enough.
"We will learn what the further plan is now."
He also stated: "You saw the class of the team in our goals, we also gave very little away.
"We tried to stabilise after a difficult and emotional period. We wanted to get players performing at their best, we got the right feeling to them and got them believing in themselves.
"This spell was a big responsiblity, I took it very seriously. I wanted to help and get United into a better place, that was my goal. With three wins and a draw it's a standard where you want to grow to as a club.
"The connection with the fans was there, I really felt it. This is what United is really about."