The club's former striker was appointed as interim manager of the Red Devils at the end of last month following Erik ten Hag's departure, and he led the 20-time English champions for four matches.
Man United posted two wins over Leicester City in the EFL Cup and Premier League, while they also overcame PAOK in the Europa League, in addition to drawing 1-1 with Chelsea in the league, under Van Nistelrooy's management.
The Red Devils beat Leicester 3-0 in England's top flight on Sunday, and Ruben Amorim will now take charge on Monday, with the Portuguese arriving from Sporting Lisbon.
Van Nistelrooy's future is unclear, with the Dutchman still not sure whether there will be a role for him at Old Trafford under Amorim, who is bringing his own staff with him to Old Trafford.
Van Nistelrooy is now stepping aside for Amorim at Man United
Bruno Fernandes and Alejandro Garnacho were on the scoresheet against Leicester, while an own goal from Victor Kristiansen also helped the Red Devils win just their fourth league win of the campaign.
"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," Van Nistelrooy told BBC Sport.
"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.
Van Nistelrooy says he took Man United role "very seriously"
"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.
"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."
Amorim's first game in charge of Man United will be against Ipswich Town on November 24, while his first fixture at Old Trafford will be against Bodo/Glimt in the Europa League on November 28.