A crowd of 16,708 were present at Old Trafford as United beat City 4-0 to move within a point of clinching the Barclays U21 Premier League title.
Three arrests were made by Greater Manchester Police following incidents at the ground
The three people concerned were subsequently de-arrested but the clubs will remain on alert with the sides due to meet again at City this season.
That could mean increased security and segregation at the return fixture
A date for that game is still to be announced but it is due to be held at the 7,000-capacity City Football Academy stadium.
A statement from City read: "We are aware of crowd disturbances at Old Trafford last night involving both sets of supporters.
"Club officials are liaising with Greater Manchester Police and Manchester United FC over this situation and will assist with their enquiries."
The two clubs liaised prior to the Old Trafford game to ensure rival supporters were segregated.
A United statement read: "There was a minor incident at last night's U21 game across segregation lines from a small number of fans, after United scored the third goal.
"Stewards resolved the matter quickly
The fans that have been identified will be dealt through the usual channels.
"The club worked with Manchester City in advance to make sure segregation was effective
Police reported some minor disturbances outside the ground after the match."
On the actual disturbances, police have clarified what occurred.
A statement read: "At around 8.50pm on Tuesday May 12 2015, police were called to Old Trafford by stewards following reports of unrest between fans who had been attending a Manchester United U21 versus Manchester City U21 match.
"Officers attended and detained a 13-year-old boy inside the ground on suspicion of pitch encroachment
He was later de-arrested and will be dealt with by summons.
"A 15-year-old boy and 19-year-old man were also detained outside the ground on suspicion of assault, but both have now been de-arrested pending further enquiries."
Source : PA
Source: PA