The match ended with Forest slipping out of the Champions League qualification spots, falling to sixth place.
The club has since denied any animosity between Marinakis and Espirito Santo, expressing their disagreement with the way the incident was perceived by the media and pundits.
"For Evangelos Marinakis, the club is not just a team - it's a family," the statement said.
"He cares deeply about each member of the team, and his reaction on Sunday was a result of that care and concern. He saw the incident as a reflection of the team's values and unity, and he felt compelled to act.
"Marinakis' actions were a demonstration of his leadership, driven by his genuine concern for the player's well-being. When he saw the player struggling in pain, he couldn't just stand by and do nothing. His instinct was to go onto the pitch and show his support.
"The truth is, there was no confrontation between Marinakis and Espirito Santo, or anyone else on the field or in the stadium. Everyone was frustrated that the medical team allowed the player to continue playing while injured.
"The club urges former coaches, players, and other influential figures in the sport to be more thoughtful and considerate in their comments, especially when they don't have all the facts. Let's prioritize the player's welfare and show the same respect that we demand from others."