Ralf Rangnick condemned the behaviour of some Leeds fans after Anthony Elanga was hit by a missile as he celebrated scoring Manchester United's third goal.
The United players were also targeted as they celebrated Harry Maguire’s opener and at half-time and Rangnick went on to the pitch to act as peacemaker when there was a melee.
"As far as I know, there is some investigation going on from Leeds United," said the United boss.
"Anthony Elanga looked well and was happy about scoring his goal. Obviously, things like that should not happen, this game, even more so.
"The atmosphere was great, at times we had to cool down things on the pitch.
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"This is what I did when I walked onto the pitch, I didn’t want anything to happen, no yellow or red cards. At times like this it’s important to cool things down."
Leeds boss Marcelo Bielsa also condemned the missile throwing, saying: "Any excess other than sporting shouldn’t be approved."
Substitutes Elanga and Fred scored for United after Leeds netted twice inside a minute to wipe out their 2-0 half-time lead and Rangnick praised his side’s character.
United are four points clear in fourth and the German said: "We knew it was important to win.
"Today it was important not only that we won, but the way we reacted after conceding the equaliser. That was the best possible answer the team could give.
"It was perfect in regard to maturity and unity.
"A game like this one, you can only win as a team and the mentality of a team, apart from the three points, was the most important thing for me."
Maguire added: "We needed to start the second half better, for sure.
"They came out right on top of us; their first goal is obviously really lucky and it got them right back in it and then they scored a good goal.
"We had to fight back and stick together; we knew it was a tough place to come but we knew we had qualities and could hurt them.
"We said at half time we needed to score more in the second half and we managed to do that."
On the conditions at Elland Road, Maguire noted: "They were really bad. We came out at the start of the second half and tried to play the same way, but got caught in it.
"It was old school, I'm sure it was good to watch but thankfully we came out on top."
Leeds, meanwhile, remain 15th - just five points clear of Watford in 18th.
Discussing his team's performance, Bielsa added: "In the first half we started well and ended well but didn't manage to score.
"In the moments we lost dominance they scored. After we got back level we had the chance to go 3-2 up and straight way they went up and scored again.
"We played better trying to get back into the game than when we were trying to keep a result but something has repeated that is difficult to resolve.
"We have to defend better."
