The Uruguayan sees the Wearside club sitting at the foot of the table, seven points from safety, with six fixtures remaining in the campaign.
Poyet's side has lost five matches in a row, which has brought about a crisis of sorts, but he only has to look across the water to Tyne-Wear rivals Newcastle who have been beaten in five of their past six outings but have managed to remain ninth.
"The most important part, which is the fans, they love it, they love football and they are desperate to do well," said Poyet when asked how to describe the difficulty of managing one of north east England's biggest two clubs.
"Go across the river and go to Newcastle - they are in an unbelievable situation in the table and there is a nightmare.
"Can we change over? Because that is a great problem to have, to be ninth?
"Why? Because it's that drive to get better all the time and to be always on top and it doesn't matter how many games you have won in the past because you need to win the next.
"That part of football, I love it because it's the best way to do it, to try to get better all the time.
"In terms of mentality for me, it's perfect, the north east. It's always better if you finish ninth instead of 10th, and I am like that.
"The problem is at the moment it is so bad that it's not enjoyable, so the idea is to make sure that we don't put ourselves in this situation anymore.
"It doesn't matter who is the manager, I am talking about the club now, the club itself."
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