The Italian was dismissed last month after failing to win any of Sunderland's first five games in the Premier League this season, with Kevin Ball taking temporary charge.
He told The Mirror: "I can't say too much about that because the club have told us not to.
"Under Paolo, the players did have some good times but the club decided to change things, so it's down to us to improve our results.
"We need points quickly, otherwise we will end up being cut adrift. There's plenty to play for, so hopefully we can climb the table."
Poyet arrives at the Stadium of Light with the Mackems rock bottom of the table with one point from seven matches.