Nine men were arrested over a pitch invasion and flares being thrown during City's 3-0 loss at Sixfields.
The club has said that the "repeated disruptions" were "unacceptable".
A Sky Blue Trust statement said: "We do not condone anti-social and illegal acts such as the throwing of smoke bombs and multiple pitch invasions."
The statement continued: "We do understand, however, that it was entirely the result of frustration and desperation and that many supporters are simply at the end of their tethers feeling powerless and ignored.
"While peaceful protests and petitions have attracted national attention and sympathy, they have seemingly been ignored by Sisu and [chairman] Tim Fisher and this once great club is in now in total disarray and turmoil.
"The scenes were ugly but borne of desperation and passion. The Trust urges all fans to keep any protests lawful and ensure these scenes are not be repeated."
Coventry fans have held a number of protests against the club's owners this season, with December's EFL Trophy second round win over Crawley attracting a record-low home crowd.
The Sky Blues are without a League One victory since 1 November and have only won four times all season.
A Coventry City fans' trust says disruption at Saturday's defeat by Northampton was caused by "desperation" with the club's owners, Sisu.