A Kilmarnock director says she was "horrified" by the actions of Rangers fans who invaded the Rugby Park pitch and damaged parts of the stadium.

Four men were arrested after Connor Goldson's 91st minute header secured a 2-1 victory for the Ibrox side.

A roof covering disabled away supporters caved in, resulting in one fan being injured.

Rangers condemned the actions of their fans but said they had raised concerns about safety inside Rugby Park.

Footage on social media also emerged showing a rammy before the match, with fans charging into the ground without using the turnstiles.

Kilmarnock are planning on charging Rangers for the damage, with the club saying it has no intention of increasing the Glasgow side's ticket allocation for future matches at Rugby Park.

Club director Phyllis McLeish said: "We were horrified at what we saw. We already had our team in to start our internal investigation.

"We have reached out to Rangers to hopefully work together to ensure the safety of both sets of fans for the next time they come and to learn some lessons.

"We are looking at some different measures for next time. We don't have a cost yet. Prior to the incident, we thought we had adequate measures but we will review this."

Ms McLeish said security searches led to supporters becoming inpatient in the queues before the game.

She said: "There was already two-thirds of the away side in but I think this was just impatience and there was a 60-second breach that was dealt with fairly quickly.

"The fans have breached through a manned ticket gate. There weren't any injuries - it was dealt with very quickly and brought back under control.

"There was heavy searching being conducted yesterday and unfortunately that did lead to some delays. Fans need to be aware of this for the season."

Ms McLeish added: "The last game of last season it went to one stand for the Rangers allocation.

"This board has made a commitment that the Moffat Stand, which is the family stand, will remain the family stand for every game. It's back in Killie hands and is staying in Killie hands."

When questioned if Rangers will be billed for the damage, Ms McLeish said: "I would think that's safe to say but we haven't concluded anything yet."

The SPFL has hit out at both incidents, stating it's conducting investigations with the police as well as Rangers and Kilmarnock.

A spokesman said: "The scenes at the end of the game at Rugby Park were simply unacceptable.

"The passion and energy of Scottish fans is a huge asset to the game, but nobody wants to see them invading the pitch - their place is in the stands.

"We will be working with Police Scotland and both clubs to investigate the incidents at the game, including turnstile and ticketing arrangements and will be studying CCTV footage to see what additional actions are required."

A Rangers spokesman said: "Rightly or wrongly a gate was forced but the real cause of the serious congestion and crushing which occurred outside the stadium before and after kick off cannot be disguised. The failure of Kilmarnock's ticketing system caused the problem and this has to be addressed.

"After all, it had become apparent long before kick off that there was a problem with their entry system which resulted in a safety issue with people fearing they were in danger of being crushed. This is not the first time Kilmarnock's system has failed.

"However, Rangers does not condone the behaviour of those fans who invaded the pitch and who caused the damage to the facility housing disabled supporters.

"The appropriate action will be taken to deal with those who can be identified but it should be pointed out that Rangers had made Kilmarnock aware of concerns over facilities for the disabled at Rugby Park."

Kilmarnock are believed to dispute Rangers' claims about their ticketing system and concerns raised.