The Black Cats boss revealed that he saw the Reds star in action in his formative years back in their homeland, and claimed that he didn't see the potential.
Suarez, who joined the Anfield side in January 2011, has since blossomed into one of the leading strikers in world football, and scored 31 goals last term en route to winning the PFA and LMA Player of the Year awards.
The Mirror quotes Poyet, who featured for both Chelsea and Tottenham Hotspur during his playing career, as saying: “I went to a friendly game. The big teams play against each other in the summer, and it was a game between Penarol and Nacional.
“Suarez played all right, but not for one minute did I think he would be this good. He was a power striker, playing up front on his own but nothing like the striker we see today.
“I doubted him, but I was wrong! Now people ask: is he the best Uruguay has produced? I say yes, why not? When he came to England and started playing, I thought ‘Mama mia what a player.'"
Suarez is in a race against time to be fit for Uruguay's second World Cup game against England on Thursday.
The 27-year-old underwent knee surgery at the end of May, and hasn't played since Liverpool's final day of the season against Newcastle United.
La Celeste head into the game needing a win after their 3-1 defeat to Costa Rica on Saturday, but Roy Hodgson's side are also just as desperate for the three points after their 2-1 reverse to Italy on the same day.