The Black Cats have suffered five consecutive defeats to leave them seven points adrift of safety, while the Magpies sit ninth, 21 points better off.
Poyet's future at the Stadium of Light has come under question and the Uruguayan has confessed that he does not know whether or not he will still be in charge of the club next season.
He has attributed this pressure to managing in the football-mad world of the North East, where his nearby counterpart Alan Pardew is also the subject of scrutiny following three heavy losses on the bounce.
However, Poyet has hinted that Newcastle's problems are nothing compared to those of relegation-threatened Sunderland's.
He told reporters: "The most important part, which is the fans, they love it, they love football and they are desperate to do well. 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."
Sunderland travel to the Etihad Stadium to face title-chasing Manchester City on Wednesday.