The Black Cats, who do not play until Monday night when they travel to White Hart Lane to take on Tottenham Hotspur, saw their survival hopes damaged by wins for West Bromwich Albion and Fulham yesterday.
Poyet's side do have at least two games in hand over all of the teams around them in the table, but with away matches against the likes of Manchester City, Chelsea and Manchester United to follow Monday's trip to Spurs, their chances look bleak.
When the Uruguayan was asked whether his side would need to do something unexpected to survive, Poyet told PA: "Yes, yes - but I think it is possible. I remember clubs in the past - I am not going to talk about names - they have played five or six games at the end of the season against teams who were playing for nothing and they won four or five.
"People say it's incredible, a miracle, but it depends what the there teams put on the pitch and what you do. But it can happen. I suppose I would try as a professional not to alter the end of the season, but if a team goes down early and they make seven changes to try things for the following year, I wouldn't blame them because they are trying for themselves.
"Now that can affect the result of that game and then everybody is blaming somebody else. But a the end of the day, you have got 38 games, it's you. You cannot blame the rest for what they do because it happens during the season when someone is playing in the Champions League and chooses to make five changes in midweek. Nobody remembers those, they only remember the last three or four when people are already out of any possibility."
Sunderland are now seven points adrift of safety with eight games left to play.