Sunderland say they are "extremely disappointed" about the alleged conduct of a "small minority" of Coventry City fans during Sunday's Championship game.
They said objects such as pyrotechnics, bottles and coins were allegedly thrown towards home fans in the North Stand.
In a statement, Sunderland said police had started an investigation to identify the people responsible.
BBC Sport has contacted Coventry City for a response.
The incidents happened just days after the Premier League and the EFL introduced new measures to clamp down on fan disorder going into the new season.