The Argentine has been a prominent figure in Poyet's side since joining from Estudiantes in January - making 21 appearances in all competitions.
After making a slow start to life as a Black Cats player, the Uruguayan boss believes the defender has made huge strides since joining - admitting that he played out of position for the majority of his spell.
"(Vergini's) form pleases me a lot for different reasons," he told the Journal.
"Firstly because I brought him here but also because I know him as a person and a player and I know how important it was for him to succeed in England.
"He was playing out of position so it is even more impressive what he has done. If you know the player and how much he is willing to play, you want to give him that opportunity.
"Everything came at the same time for us - Phil (Bardsley) was suspended, Celustka was injured and Craig Gardner was ill so he was the only option as a right-back. I saw him two or three times there so gave him the opportunity," Poyet added.
"It was almost unfair on him because if he plays badly there, it might kill him. He didn't and you have to give him an incredible amount of credit.
"He deserves it, he's a terrific lad and it will be nice to sit down after we've finished the season and have a good chat with him."
Along with Vergini, doubts have surrounded the long-term futures of Jack Colback, Phil Bardsley and Sebastian Larsson.
However, it is understood that the trio are currently locked in talks with Sunderland - with the Wearside club hoping to conclude negotiations quickly.