While they have two matches in hand on bottom club Fulham and 18th-placed Cardiff City and one over West Brom and Crystal Palace, they face a daunting three weeks which sees them pitted against Tottenham Hotspur, Everton, Manchester City and Chelsea.
Having failed to win in their last six matches since a morale-boosting 3-0 victory over bitter local rivals Newcastle United at the start of February, Sunderland’s future could effectively be sealed weeks before the season draws to an end.
Uruguayan Poyet, who replaced controversial Italian Paolo Di Canio as manager in October, said he will resign from his post if his players “give up” in their battle against the drop.
“If my team give up, I’ll leave,” he told a news conference following the loss at the Stadium of Light, where Andy Carroll and Mohamed Diame put West Ham 2-0 up before Adam Johnson pulled a goal back with 25 minutes remaining.
“Nobody needs to sack me, I’ll leave on my own, OK?
“If you see this team giving up before the end of the season, you won’t see me here.”
Poyet joined Sunderland with the team seemingly marooned at the foot of the table with one point from seven matches, but sparked something of a rival which saw them reach the Capital One Cup final, where they lost to City, and the quarter-finals of the FA Cup.
Having taken only one point from their last six matches, however, means their six-year stay in England’s top flight is in real danger of coming to an end.
Hope remains in the equally poor form displayed by their rivals for avoiding the drop, and the fact that the side are capable of turning in a decent performance, as shown by last week’s narrow defeat by leaders Liverpool.
“If we play like we play against Liverpool and today in the next eight games, we’re going to have a great chance (of surviving),” Poyet said.
“The crystal ball, I can tell you, is not in my house. I’m not going to try and read the future because I’m not very good at that.
“What I believe is that I need to convince the players to keep doing it and defend this club to the end, to the last minute – to try their best.
“If everybody does the same, who goes out? The three worst teams in the league.”
(Reporting by Josh Reich, editing by Sudipto Ganguly)