The south-coast club's executive chairman Nicola Cortese resigned on Wednesday, leading to doubts about manager Mauricio Pochettino's future after the Argentine had previously said he would leave if Cortese were no longer at the club.
However, the former Espanyol manager confirmed on Thursday that he has no intention of walking out on Southampton and will be in charge for the weekend's Premier League clash at the Stadium of Light.
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"It can be either way, depending how they perform - it could go either way," said the Uruguayan.
"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."
Pochettino's side have been a surprise package this season and Poyet has been impressed with the impact the 41-year-old coach has made in such a short space of time, lauding his faith in the club's host of young starlets.
"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," Poyet added.
"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."