After their 2-2 draw with Leicester City, Marinakis stormed onto the pitch and was seen in furious conversation with Nuno.
In a statement later, Nuno said: "We were frustrated around the injury of Taiwo (Awoniyi) and the medical staff's misjudgement on Taiwo's ability to continue the game.
"This is natural, this is a demonstration of the passion we feel for our club.
"Today is a day for celebration, because after 30 years Nottingham Forest is now guaranteed to be competing on the European stage once again - a promise I made to our supporters when we achieved promotion.
"With two more games to go in the Premier League, we must keep believing and keep dreaming, right to the final kick in the final game. We are extremely proud and close to Nuno and the team, and we must all celebrate the historic achievements of this season."
Confusion over Awoniyi
Meanwhile, Nuno in his post-match media conference insisted there were no issues between the two men.
He explained, "It (the conversation with Marinakis) was due to the situation and the confusion over the substitution of (Taiwo Awoniyi)," Nuno said.
"We made a (different) sub and after that we played with one man less so that frustrates everyone.
"When a player is down, you get information that he is OK to continue, then we make a sub and it turns out he can't continue. We are all frustrated with that.
"Football is emotions. It's difficult to control (and) especially when we had so much expectation and the fans were incredible."
Marinakis wants Forest to be a big club
Asked about his feelings about the public confrontation, Nuno remained calm.
"It is because of the owner and his passion that we are growing as a club. He pushes us. He wants us to be better," Nuno added.
"It is his passion and desire to be a big club - 30,000 people felt the same today. For sure, many of them would go on the pitch and shake us down.
"Us as a club, we owe a lot to the Marinakis family."