The 46-year-old Uruguayan and his players face a huge task at Anfield on Wednesday evening as they attempt to bounce back from an abject display in Saturday's 2-0 Barclays Premier League defeat at Norwich which left them deep in relegation trouble.
They will arrive on Merseyside to confront a Reds juggernaut piloted largely by Suarez, whose haul of 28 league goals to date this season is two more than Sunderland's entire squad has managed.
Poyet has been aware of his countryman for some time, but admitted he did not expect him to catapult himself into the highest echelons of world football.
The Black Cats boss said: "I saw him once in a summer friendly game. He was just starting, I think he was 17 or 18. He was a powerful striker playing on his own, but of course, not the player we are seeing today.
"To be honest, I wasn't even thinking he would be so good. He played a decent game, but now he is on another level.
"Now you can compare him with the top players in the world because he makes the difference somehow."
Poyet added with a smile: "It's going to be tough. I hope he gets ill tonight."
Suarez and strike-partner Daniel Sturridge have plundered a total of 47 league goals between them to fire Brendan Rodgers men firmly into the title race.
However, Poyet firmly believes they would be languishing in mid-table had it not been for the Uruguay international.
He said: "I am not surprised, that's why they have got a chance. Without Suarez, they would probably be in mid-table.
"It's not about how they play, how they defend, how they pass the ball, it's about having a player who is going to be voted the best player of the year by everybody, if we are honest."
By contrast, Sunderland find themselves entrenched at the opposite end of the table with goals at one end at a premium - midfielder Adam Johnson's seven in the league equals the sum total managed by strikers Steven Fletcher, Jozy Altidore, Fabio Borini and Ignacio Scocco - and a depressingly familiar occurrence at the other.
With Fletcher nursing another ankle injury - Poyet admitted the prognosis is not good - and loan signing Borini ineligible to play against his parent club, 20-year-old Connor Wickham has been recalled from Leeds.
However, while knowing his team needs to improve significantly with games running out fast, the South American insists he is not worried by their plight.
He said: "No, I am not worried because I knew the first day I got the job that it was a very big challenge, if not nearly impossible.
"Now we will see. We have got 10 games. I am not going to hide. I am going to be here and I am going to take responsibility, but let's wait and see.
"In the same way as I ask the fans to wait until the last game of the season to give their opinion on the team and the signings and individuals, I am going to do the same.
"Until the last game of the season, the last second against Swansea, I am going to be here believing it's possible because if not, it's not worth it, let's be honest.
"I am not going to be here just to have a job. I am here because I believe that we can be better than at least three teams. That's the aim from here to then."