The Hoops skipper’s shot from the edge of the box was deflected past Daniel Bachmann in the Killie goal, sparking wild scenes in the away end that led to a number of visiting fans celebrating on the pitch with the Celtic players.

Brown was given a second yellow card and sent off for his reaction to the goal, which Rodgers insisted was “harsh”.

• READ MORE - Kilmarnock 0-1 Celtic: Scott Brown nets late winner and is sent off as Hoops extend lead

Celtic fans stream onto the pitch following Scott Brown's late winner. Picture: SNS Group

The Northern Irishman said after the match: “When I looked around [after the goal], there was a bit of a melee going on. Supporters had come on to the pitch, which we don’t want to see.  “I understand the emotion of it all. But I didn’t see so much of it, I had to reorganise very quickly because we were down to ten men.”

The Celtic manager also condemned an earlier incident when Kilmarnock substitute Kris Boyd appeared to be struck by a coin while warming up.

Veteran striker Boyd was also reportedly subjected to sectarian abuse from some sections of the crowd.

Killie manager Steve Clarke was unaware of the reported coin-throwing incident but Rodgers said: “Any behaviour like that is not acceptable at all, I think we would all reinforce that.”

Sky Sports pundits Kris Commons and James McFadden branded the incident “disgusting”, with Scotland national team assistant coach McFadden adding: “It’s unacceptable. Kris has got his opinions and if you want to give him stick that’s fine.

• READ MORE - Kris Boyd ‘hit by coin and subjected to sectarian abuse’ during Kilmarnock-Celtic clash “He’s a grown man, he likes to give it out and he can take it but to throw coins - there’s no place for it. Absolutely no place for it. It’s disgusting.”

Former Celtic midfielder Commons added: “This isn’t an isolated incident - it needs stamped out very, very quickly.”

Brendan Rodgers bemoans Celtic fans’ pitch invasion and condemns Kris Boyd coin incident