Some Latics fans bought tickets in the Cheadle End at Edgeley Park and were involved in fighting with some home fans after Andy Liddell gave the visitors the lead.
A club spokesman said: "Stockport County does not condone violence of any kind. Those involved in leading the isolated incident of trouble have been identified.
"And the club would like to thank the stewards on duty for their prompt reaction which also gained praise from the referee.
"In a situation which was difficult to manage, the club are satisfied that the number of Oldham fans who succeeded in gaining tickets to County areas was reduced to an absolute minimum.
"County have an excellent record of safety in the stadium which we will work hard to protect."
Jim Gannon's side came from behind with a spirited second-half performance to win 3-1 and will be full of confidence for tonight's Johnstone's Paint Trophy tie against Bury at Gigg Lane.
But they will be without keeper Owain fon Williams, who has joined up with the Wales Under-21 squad.
Fraser Forster, a 6ft 6in keeper, who arrived from Newcastle on a month's loan and will start.
Bury are unbeaten in the league and boss Alan Knill is determined the Shakers take the tie equally seriously.
Knill said: "This competition provides the opportunity for both sets of players to play at Wembley, and for the clubs a large pay day if you can make it to the final.
"There has always been a lot of talk about this competition but for the teams at this level the opportunities to play at Wembley are very limited so it has to be taken seriously."
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