The Black Cats were dealt a blow in their hopes of staying in the top flight following last night's 2-1 defeat to West Ham United.
The North-East outfit are now four points adrift of safety in the table, with a game in hand on 17th-placed West Bromwich Albion.
"If my team give up, I'll leave," Poyet told reporters. "Nobody needs to sack me, I'll leave on my own, okay? If you see this team giving up before the end of the season, you won't see me here."
Sunderland's next fixture is away to Tottenham Hotspur on Monday, April 7.