The Black Cats undid their good work over Christmas with a depressing 1-0 home defeat by Aston Villa on New Year's Day which left them still propping up the rest of the Barclays Premier League and four points shy of safety.
Villa's visit to the Stadium of Light heralded a run of games the Wearsiders consider winnable and therefore, an opportunity to ease themselves up the table and out of danger.
However, their one step forward, two steps back existence has persuaded Poyet that his message is simply not getting through to some of the players, and that is a situation he insists will not be allowed to continue.
The 46-year-old said: "Me, I am the head coach, I coach the players I have got the best I can.
"For moments, it looks like we are getting it and getting better, and for moments, it looks like I am coming from another planet, which is difficult to accept.
"The best teams in the world play one game, one game. They know why they are playing, what they are playing for and everybody does the same.
"If you go on the pitch and everyone is playing their own game, it's impossible.
"I have said to you many, many times, it is not a tennis match, it's football and it's 11 and there are players we normally think are able to do things, and we are learning more and more that they are not able to do it.
"That's the only good news today, I have got a good report on some players who are not able to play a certain way, which is going to be difficult for them because we will play that way, so the problem is for them."
The Black Cats have already signed Fiorentina full-back Marcos Alonso on loan for the rest of the season and are currently deep in negotiations with Brighton for midfield duo Liam Bridcutt and Will Buckley.
However, Poyet knows the men already under his charge will be largely the ones who will have to do the job if the club is to preserve its top-flight status, and his message to them is stark after a seventh home league defeat of the campaign.
He said: "We had more of the ball, we had more shots, but we didn't create enough because we tried to do it too much as individuals and not as a team.
"I said it two months ago: there are not going to be heroes here, we are all in it the same and we will all be safe or we will all go down.
"Apparently, some people don't get it. They try to play their own game and they try to be in their own position and they try to do things that are not acceptable.
"It's a difficult day for me, I need to be careful what I say."
Ironically, skipper Lee Cattermole's determination to carry out Poyet's orders led to the decisive moment in Sunderland's latest reverse.
The Uruguayan has urged his players to retain possession and to pass their way up the field, but it was the midfielder's failure to control Valentin Roberge's 15th-minute square ball deep inside his own half which allowed Gabriel Agbonlahor to round keeper Vito Mannone and score the game's only goal.
Until that point, the Black Cats had been the better side, and although Agbonlahor's intervention severely dented their confidence, they thought they had dragged themselves back into the contest seven minutes after the break when Emanuele Giaccherini struck from Steven Fletcher's knock-down, only for the tightest of offside decisions to ruin his celebrations.
Villa should have wrapped up the win as the clock ran down with Christian Benteke and substitute Marc Albrighton twice going close, but a single goal ultimately proved enough.
The win left the visitors level on points with 10th-placed Hull, and match-winner Agbonlahor is hoping it will provide a platform for a new year push.
He told the club's official website, www.avfc.co.uk: "We have had a hard couple of weeks and to get a few points on the table is always important.
"It has put us up to joint 10th, so it gives us a little bit of breathing space. It's a good way to start the new year and we have got to continue it.
"We had a lot of chances and could have won the game by three or four. But we will take the result and move on to the next game against Sheffield United."