Poyet risks losing nine players at the end of the season with Jack Colback, Carlos Cuellar, Andrea Dossena, Keiren Westwood, Craig Gardner, Seb Larsson, Ji Dong-won, David Vaughan and Phil Bardsley all out of contract.
However, the Black Cats boss believes the players will have to be patient, as the club cannot afford to offer long-term deals until their future in the Premier League becomes clearer.
"I think, in this situation, the players are clever enough to realise it's going to take time," Poyet told the Sunderland Echo.
"We might not be able to do it earlier because, at the end of the day, we don't know where we're going to be.
"Those who play week in, week out, will have it easier than those who are not.
"But overall, yes, we've got too many players who are out of contract and we've got to slowly start sorting it out."
The Uruguayan has promised his players that they will not be misled and will let them know if they are going to be surplus to requirements
Poyet added: "I'm calm. If I was a player here I'd be calm too. They know where they're standing. That's the way I work. I hate promising things.
"I don't want to tell players they are going to be here for 10 years and then we offer him a six-month contract.
"I tell him the truth of how much he counts for me, what is his standing, what opportunity he'll have and what he needs to do if he wants to stay here."