"I am confident we will stay up and I'm confident that you will see in years to come where Forest will be," Marinakis told BBC Sport.
"It's a great team, it inspires us and we want to do more and you will see in the years to come that we have big dreams for Forest.
"It is stressful because of what has been happening since the beginning of the year with some decisions and points deduction.
"It's not fair what has happened so far.
"Referee decisions have cost us points and this is something that has been repeated and repeated and what we expect for the Premier League and referees is to correct these mistakes.
"It's a pity as we have a great appetite for the club and I never give up."
Marinakis has seen his Greek club Olympiakos reach the Europa Conference League final after victory against Aston Villa home and away in their semifinal.
He added: "It was a very big achievement for our players, our manager and fantastic crowd, they all supported. There's something magic in this stadium in Piraeus, you have these positive vibes that help you and you feel a winner from the very beginning."