Despite victories over Newcastle United and Manchester City following Poyet's appointment as head coach in October, Sunderland are rooted to the foot of the table, five points from safety.
However, Poyet refuses to accept that relegation is inevitable.
"My belief hasn't diminished since I came here," said the Uruguayan ahead of Saturday's meeting with 17th-placed West Ham.
"I believe I can (keep Sunderland up). I see things that are getting better and that we are good enough to get two or three wins, or maybe a draw, before January 2.
"From what I know, nobody at the club has given up.
"It would be silly to give up because there are so many games."
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