Saturday's pitch invasion by Oldham fans after the 2-1 League Two defeat by Colchester United is to be investigated by the Football Association.
Fans invaded the Boundary Park pitch to protest at the running of the club, with the Latics bottom of the English Football League after the loss.
Oldham Athletic Supporters Federation's statement called for "calm heads".
The group said it "understood" fans' feelings but also added it "cannot endorse encroachment" on the pitch.
The statement continued: "Many of us have felt for a long time now that the football club has been slipping further and further into danger due to poor recruitment, heavy-handed management and alienation of supporters.
"Yesterday's overflowing of emotions by some supporters was a direct result of that frustration and we want to assure you that we are planning our next moves in close liaison with [fellow supporter group] Push The Boundary and other supporter groups, starting on Monday."
Four defeats from four in the league have seen Keith Curle's side slump to the foot of League Two, with just two goals scored.
"The supporters, if things aren't going their way, they will show their disappointment and the way they show it is being vocal," Curle told BBC Radio Manchester.
"I understand their frustrations, and feel for them. We're going to work harder. We're down to the bare bones and we've just got to deal with it."