The Football Association is looking into the incident in which Anthony Elanga was hit by an object thrown from the crowd.
Both sets of supporters made distasteful chants.
Nine people were arrested for throwing missiles, according to West Yorkshire Police.
There was no significant disorder and no injuries were reported to any players or fans, the police said.
A group of 70 away fans were issued with dispersal notices prior to the match after turning up without tickets.
In the first game in front of fans at Elland Road since October 2003 Elanga scored his side's fourth goal with two minutes remaining to confirm the victory for the men.
Arrests at football matches across the top five English leagues are at their highest levels in years, with fan disorder getting worse, according to the UK's football policing lead.
There were more than 800 football-related arrests in the first six months of the season.
As far as I know, there is an investigation going on at Leeds United. I don't think anything happened in the end, said Manchester United's interim manager.
Elanga looked well and he was happy about his goal. I think things like that should not happen in this game. The atmosphere was great.
The incidents involving objects being thrown were condemned by the boss.
He said that any excess other than sporting should not be approved.
The chief football writer is Phil McNulty.
The poison of the rivalry boiled over in a vicious atmosphere when Elland Road staged a game between the two clubs in front of fans.
There was a large police presence around the stadium before and after the game, as well as in the city centre hours after the game, which is a sign of the animosity between the two sets of fans.
The tone was set from the moment Manchester United's players came out to warm-up, but this was a very mild message compared to some of the vile verbal exchanges from opposing supporters.
The captain of Manchester United and some of his teammates were shepherded away from the Don Revie Stand and angry fans after their first goal.
The smell of fireworks hung heavy in the air, but it was the last two goals scored by the visitors that saw the players in danger.
After Fred put Manchester United back in front at 3-2 with similar treatment meted out after the substitute, recovered after being struck, the fourth himself added.
The atmosphere inside the stadium and the actions of the supporters has led to a full investigation after the game, which was played out in a torrent of rain.
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