Poyet does not want an apology from his top scorer but a change in his reluctance to “clarify things”.
Forster came into conflict with the manager eight days ago, following a story on Sky Sports News that he had handed in a transfer request.
The 36-year-old, one of several players out of contract in the summer, then issued a statement to The Argus the same day, implying there was no route back with “no contract in the offing.”
He said: “It is with great regret that this outcome has been reached, as I have enjoyed my time with Brighton and would have liked nothing more than to extend my stay.”
Forster was dropped for the game at Leyton Orient the next day and left out of the squad again for Tuesday's home match against Huddersfield. Poyet said: “I have no problem with Nicky Forster, he does not even need to apologise, but I want him to clarify things and at the moment it looks like he does not want to do this.
“He did not put a transfer request in to us. He put the statement out via Sky Sports and the local paper last week, not the club. He made a statement as if he had left the club. All the time that is the case, then he is not in the team.
“We are not a one-person team. I have 25 other players to consider and, if one player acts like that and I take no action, then all of a sudden I have 25 players acting like that.
“Myself, Mauricio (Taricco) and Charlie (Oatway) sat all of the out-of-contract players down on January 15th and told them all that we would not be in a position to discuss contract extensions until such time as we are safe from relegation.
“Of course, these players are all free to talk to any other clubs at any time they like. That is the risk I am taking and I am prepared to take that risk.”
Albion announced last month that defender Adam El-Abd had been awarded a new deal.
Poyet, speaking at a fund-raising fans' forum on behalf of the club's community department at Burgess Hill FC, said: “The offer was made back in December, a long time before we told the players that we would not be holding any more contract talks. “The reason why I wanted to offer Adam a new contract is very clear. He is the most valuable player for me at present.
“He is the best at defending at the club. I know that this view is not shared by everyone but you have to look at the whole game and not just when players are on the ball.
“When we are defending he knows what his job is and he does it. When we are attacking he knows what his job is and he does it. He may not be the best on the ball but he is a very good footballer.”