A section of the perimeter fence gave way, with several stewards then starting to help people get out through the gap. Riot police, however, stopped fans coming out of the stand and used tear gas to force them back.
The hole in the fence was then closed using a chain and police stood their ground in front of the stand.
French police claimed it was the United supporters who were to blame by selling false tickets, which meant a stand behind one off the goals was crammed to over capacity.
A French police spokesman told AFP: "English supporters sold false tickets which meant the stand which was reserved for them was crammed full," adding the "Trannin" stand behind one of the goals had 5,000 fans in it instead of 3,500.
"We had no choice but to intervene. When police found themselves in a situation they could not control, they had to use tear gas.
"We coped as best we could with the situation, we had to intervene. In the end there were only some minor fights, arrests of drunken fans and several injured England supporters," the police spokesman added.
Manchester United are calling for eye witness accounts, while Caborn has urged European football's governing body Uefa to ensure safety in stadiums following the crowd trouble in Lens.
A Uefa spokesman told AFP early Wednesday they would wait for reports from the match delegate and the referee, which must be sent within 48 hours, before making a statement.
Not up to standard
Lille play their European matches at nearby Lens because their Metropole stadium does not meet Uefa standards.
Anti-riot police arrest Manchester United fans
on the pitch in the match against Lille [AFP]
"I think some of the grounds are not coming up to what even Uefa are saying are the minimum standards and I think one's got to be asking Uefa are they now going to be taking action with those grounds that are not coming up to the standards?" Caborn said on LBC radio
"Not a few hours before the match but weeks before the match so they go out, they look at those grounds and indeed if they're not up to standard then Uefa, by their own code, ought to be taking action.
"There are a number of grounds where Champions League matches are being played that don't come up to the standard of Uefa.
"We'll be raising it with Uefa in a very practical way because the independent football commission have a series of recommendations which, if followed, situations like Lille won't happen," Caborn added.
Media in Britain likened the drama to the Hillsborough tragedy in 1989 when 95 people died after being crushed against the perimeter fencing in an FA Cup semi-final between Nottingham Forest and Liverpool in the neutral venue of Sheffield Wednesday's stadium.
Perimeter fencing was subsequently banned in English stadiums.