The Saints are due on Wearside on Saturday with the repercussions of executive chairman Nicola Cortese's resignation still reverberating on the South Coast.
Manager Mauricio Pochettino, whose future had appeared to be thrown into doubt by the departure of his close ally, confirmed he would be staying on Thursday afternoon but the last few days have served as a far from ideal preparation for a trip to the Stadium of Light.
However, Poyet will not allow his players to be fooled into thinking they will face a club in disarray as they attempt to record back-to-back Barclays Premier League victories for the first time this season.
The 46-year-old said: "It can be either way, depending how they perform, it could go either way.
"When people say it doesn't affect the players, it does. But that doesn't mean it affects you badly, it can affect you the other way, so we will see what happens on Saturday.
"It's difficult, a strange, unique situation, what is happening at Southampton. It depends what the consequences are, you never know. It's unexpected."
Indeed, Poyet will prepare his players for what he believes will be a "unique" challenge against Argentinian Pochettino's side, which currently sits in ninth place in the table, 13 points better off than this weekend's opponents.
The Uruguayan said: "That's one of the best parts of Southampton this year, to have something so very new, unique - I don't think you can compare it with any other team in the world.
"They have got their own system, the way they play, very young players adapting to the style very well and trying to be consistent with a new manager.
"It's something refreshing for the Premier League, which is very welcome.
"Mauricio has adapted very well, very quickly. He knew exactly what to do, the players reacted to him. He has done very well and it has been working so far, so credit to him.
"I played against him in Spain. He was a very tough defender, Mauricio Pochettino. We had a few nice games against each other.
"He was an honest player, so I am pleased for him."
Sunderland hauled themselves from the foot of the Premier League table as a result of their stunning 4-1 victory at Fulham last Saturday and are now just a point shy of dragging themselves out of the relegation zone, something which looked a forlorn hope when Poyet arrived in the north-east in October last year.
However, while he is delighted with the job his players have done to date, he knows there is still a long, long way to go as they look for a fourth successive win in all competitions.
He said: "The idea is to keep winning because we need more points. I was trying to think about how much of the job we have done so far - I would say maybe half.
"We were really far away from everybody, everybody was looking at the table and they were writing us off completely, and now we are there in the mix, so I would like to say that half of the job is done.
"But the other half is going to be as difficult as the first. We have proved that we are able to do it, so if we maintain that level and we do on Saturday what we have done until today, we are going to be in a great position to stay in the Premier League."
Work to secure Sunderland's top-flight status is ongoing on and off the pitch with the Black Cats closing in on Estudiantes central defender Santiago Vergini.
Poyet declined to comment on the club's pursuit of Internacional striker Nacho Scocco, although there is further room for manoeuvre in that department with Ji Dong-won having completed a permanent move to German side Augsburg less than five months after the Black Cats rejected a £5million bid for him.
Poyet said: "We wish him well because for some reason, I don't know, it don't work out for him at Sunderland, so I hope it works at his next club."