He asked owner Ellis Short to block Stoke's £5m move for the 25-year-old - and Short obliged.
Poyet told the Evening Chronicle: "The chairman has been exceptional.
"It was a big decision with Lee and it was a credit to the chairman.
"The question was 'do you need Lee Cattermole?' I said yes I do. 'Well he's going nowhere,' he said.
"That doesn't happen a lot in football because it was not easy to turn down that offer."