Kilmarnock manager Steve Clarke has called for the "sensible majority" to help authorities deal with the kind of crowd trouble that marred their defeat by Celtic.

The Kilmarnock board reacted with "dismay" in a statement on Monday night following a number of issues from Sunday's Rugby Park clash.

Killie substitute Kris Boyd was hit with a coin as he warmed up, some Celtic fans invaded the pitch after their late winner and "confronted" home players, according to the Ayrshire club, and a number of seats were damaged.

Clarke said: "The worrying factor on Sunday was that people came on to the pitch. But I believe it's a criminal offence to go on the pitch, so there's plenty of cameras and plenty of faces will be on those cameras, so the authorities have to deal with it.

"You don't want anyone throwing anything. People go to football to watch the game, they should watch the game.

"Everyone keeps talking about the mindless minority, and it is. But I think the more sensible majority also have a part to play. They have to point out the mindless minority, and then the authorities can deal with it better."

Killie midfielder Rory McKenzie admitted it was frustrating to have to deal with the aftermath of the goal celebrations following Scott Brown's 90th-minute strike.

"Obviously conceding a goal that late wasn't nice and then to have Celtic fans on in your face wasn't nice as well," he said.

"The few that come in, there was no malice in it at all, most of them that I saw were young kids.

"To be fair they had their phones out. I think they were just trying to get pictures, there was no badness.

"There was four minutes added on so we wanted the game to get going because there was still a chance to get an equaliser.

"The fact that all the G4S staff were on the pitch for a minute or two, you wanted the game to get going again. That was the only frustrating thing on my part."

McKenzie added: "The coin throwing is unacceptable. As Kris said, it could injure somebody.

"I don't know whether the cameras caught who (it was) but definitely something (needs to be done), harsher bans, stuff like that, because one day it will catch someone on the corner of the eye and damage will be done.

"I spoke to Boydy after it and just after it hit him. It doesn't show you on the video, but he picked it up and there were fans on the front row who had obviously seen it and they were just standing there shaking their heads. So it is a minority."