Kilmarnock were "horrified" by the scenes that saw a disabled section roof cave in amid a pitch invasion from Rangers fans in Sunday's Premiership clash.
Four men have been arrested after the last-minute melee which followed Connor Goldson 's 89th-minute winner for the Glasgow side.
Kilmarnock director Phyllis McLeish says her club was shocked by the scenes, coming after hundreds of Rangers fans had been locked out for the opening 10 minutes of the match.
Rangers have condemned the behaviour of the fans who destroyed the disabled section, although they also revealed concerns were raised over the safety of the facility.
And the Ibrox club have released a strong-worded statement themselves and said the "failure" of the Rugby Park ticketing system caused serious congestion and crushing outside the stadium.
Kilmarnock will bill Rangers for the damage and director McLeish told stv: "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."
Killie reduced Rangers ticket allocation for games at Rugby Park for the final game of last season, halving it to 4000.
The new arrangement remained in place for Sunday's league opener - but the game was mired by problems off the field.
McLeish 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."
However, Rangers hit back strongly and a 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 Rangers had made Kilmarnock aware of concerns over facilities for the disabled at Rugby Park."
An SPFL 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."
