The Black Cats will head into Wednesday night's Capital One Cup fourth round tie against Southampton with midfielder Lee Cattermole and full-back Andrea Dossena frustrated bystanders as they each begin three-match bans.
Both men were sent off within minutes of each other in the first half of Saturday's 1-0 Barclays Premier League defeat at Hull which left the club still deep in trouble, and they will not be available again until Sunderland travel to Aston Villa on the final day of this month.
Poyet's predecessor Paolo Di Canio's attempts to enforce his brand of discipline off the pitch proved hugely unpopular during his brief, but ill-fated reign, and the Uruguayan is more concerned with the behaviour of his players on the field of play.
He said: "For me, it was a surprise. I need to analyse from the moment I came here, it was all right. I'm not saying it was perfect, but it was not bad.
"Now so many things happened in this game that I'm trying to take it as a one-off. Of course, we need to talk about it and sort it out - it shouldn't happen again.
"But we are human beings, the players on the pitch, and they are the ones who need to control themselves.
"We can talk and talk and bring in whoever you like, psychologists, psychiatrists or whatever, but then the one on the pitch is the player and the one who makes the tackle or the reaction is the player.
"If they learn, great; if they don't, then they are going to have a problem to play in the team because they are going to be more out than in."
The double suspension will force Poyet into a reshuffle for the Saints' visit to Wearside, while keeper Keiren Westwood is rated at only 50-50 as he attempts to shake off the after-effects of his collision with Tigers' defender Paul McShane at the weekend.
However, while the cup may not be the Black Cats' main priority this season, the manager is hoping the game can help to forge a level of consistency ahead of Sunday's daunting clash with Manchester City.
He said: "I try not to put it on a different level to anything, not because I want to give it more or less importance because we need to keep improving.
"We need to keep getting better. We need plenty of things, we need to do better for longer periods during the game, not only 45 minutes.
"It's another game, another important test against a very good team, so use it as another step forward. It's quite important.
"I know if you put in the balance would you prefer to win on Sunday... That's too easy.
"I don't know what is going to happen tomorrow, I don't know what is going to happen on Sunday. First things first - let's play tomorrow and try to win tomorrow."