The 46-year-old Uruguayan has spent the three months since he replaced Paolo Di Canio at the Stadium of Light helm trying to instil a brand of football which will make his side both more secure and more creative.
However, they remain rooted to the foot of the Barclays Premier League table and in severe peril following Wednesday's 1-0 home defeat by Aston Villa.
Poyet admitted after that game that some of his players were simply not getting it and has changed his methods this week with a stark warning that there is nowhere left to go.
He said: "When you get ready to be a manager, you know there are different ways of coaching or convincing players, and you have to use them all.
"Some players get it just by listening to you, some players get it by training on the pitch, some players get it by watching a video, some players get it by repetition - they are all different.
"We have been doing a little bit more of a few of the others and we are trying to address that and do different things so maybe the ones who are not getting it, they will.
"And if they don't get it this way, they won't get it, that's for sure, I can tell you. There are no more ways to coach or to manage or to teach, whatever you want to call it."
Sunderland take a break from their league travails this week as they play two cup-ties in three days with Manchester United heading for Wearside on Tuesday evening for the first leg of their Capital One Cup semi-final following Sunday's FA Cup third-round clash with League One Carlisle.
But while a degree of pressure may be lifted from their shoulders as the fight for top-flight survival is put to one side for a few days, Poyet has urged his players not to relax.
He said: "Relax? It can go either way. You can relax and go and express yourself and be at your best, or you can relax and don't care.
"It's like when you are in the dressing room and it's silence and you say is it silence because we are concentrated, or silence because we are worried? I hope it's concentration.
"Until the players are on the pitch, you don't know if it's one or the other.
"I think it's a game of football that you are playing against someone and you should go and do better than you normally do because of the difference between the players.
"Individually you can be better, but you need to be especially better as a team, and that's the only thing that can change the game."
Poyet will attempt to balance the demands of the three competitions in which his team is still involved, although he insists whoever he picks, he will send out a team of Premier League players.
Defender Wes Brown is available after completing a three-match ban, while John O'Shea was due to train with the rest of the group for the first time on Saturday following a shoulder injury.
But it remains to be seen if midfielder Lee Cattermole is involved after being substituted at half-time in midweek following the error which allowed Gabriel Agbonlahor to fire Villa to victory.
Poyet later revealed he had withdrawn Cattermole for the sake of the team with the atmosphere inside the stadium having taken a turn for the worse, and having spoken to him since, he insists the 25-year-old understands his reasons for doing so.
He said: "People will take it a different way, people will say: 'He killed him, he changed him after the mistake'.
"Well, people can think or say whatever they like, I know why I did it and it was for the benefit of the team. I explained that to Lee and I think Lee is convinced that it was best for the team as well."
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