Forest later denied Marinakis' exchange with Nuno was a "confrontation" and described subsequent reaction to the situation as "fake news".
The club said the incident was because of Marinakis' frustration that striker Taiwo Awoniyi had continued to play after an 88th-minute injury, which subsequently required urgent surgery.
"I've dished out my fair share of criticism and praise in the last 14 years of doing this job and have never come close to this unprecedented action," Neville said.
"Whilst they have every right to choose who they let into their own stadium, it's symptomatic of things that have happened over the last 12 months with the club."
Seventh-placed Forest can qualify for next season's Champions League on Sunday if they beat Chelsea at the City Ground and other results go their way.
"Personally, I think it's disappointing that a great club like Nottingham Forest have been reduced to making such a decision," Neville added.
"I wish the coaching staff, players and fans of the club all the best in their quest to achieve Champions League football."
The Premier League said accreditation was a club matter.
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