Everton Fans' Forum have contacted the club seeking "urgent answers" after many fans were caught up "chaotic scenes" trying to access the ground for the Burnley cup tie.
The group posted on Twitter on 2 November, the morning after the 3-0 Carabao Cup win, after supporters struggled to get into Goodison Park ahead of kick off.
Fans have suggested online that there was an inability to move on the streets surrounding the stadium before the game and a lack of safety as stewards were apparently overwhelmed.
The Fan's Forum wrote: "We have been made aware about, indeed many of us were caught up in, chaotic scenes in gaining access to Goodison Park last night.
"This has been raised with the club and urgent answers as to the cause of this chaos have been sought.
"Despite what was actually a very positive night for Everton as Sean Dyche's current club overcame his former side with relative ease this is an unfortunate footnote.
Nobody needs reminding of the dangers which are present when football crowds are stuck and people can't safely move around.
Whatever the cause for the potentially unsafe situation around Goodison on Wednesday should be identified as quickly as possible and contingency plans put it place to avoid a repeat.
Similarly, any lessons that can be learned need to be applied to preparations for Everton moving into the new dockside stadium.
The suggestion is that the stewards that were present were doing what they could in unenviable circumstances, but the surrounding streets had a problem.
If it is being addressed as a matter of priority from the Fans' Forum side then the hope is that the club now respond in kind and measures can be put in place to ensure a similar situation doesn't arise again in the future.
In other Everton news, a transfer update has emerged as Chelsea eye Toffees and Arsenal targets.
{{#primary_category}} {{primary_category}}{{/primary_category}} {{author_name}} {{date_formatted}} Injury Expert issues update on Everton attacking midfielder Dele Alli.