The Wearside club suffered another major setback in their battle to avoid the drop when they were thrashed 5-1 at White Hart Lane on Monday.
Lee Cattermole's long-awaited first goal for the club had put them in front, but Tottenham came roaring back with Emmanuel Adebayor scoring twice and Harry Kane, Christian Eriksen and Gylfi Sigurdsson also on target.
A fourth consecutive top-flight defeat for Sunderland leaves them bottom of the table and seven points behind 17th-placed Norwich City.
Poyet's side do have two games in hand on the three teams directly above them, but the Uruguayan pulled no punches with his verdict over their latest defeat and admitted their chances of preserving their Premier League status are remote.
He told Sky Sports: "It's very hard to take. I imagine how hard it is for the fans who travelled and everybody at the club. But there's no place to hide, I'm responsible because I'm in charge and I'll take full responsibility.
"(It is) definitely more difficult now. We need a miracle probably, something very unique. If not it's going to be practically impossible."
Sunderland still have to play the likes of title contenders Chelsea and Manchester City, as well as Everton and Manchester United, before the end of the season, meaning they will have to upset the odds in order to avoid dropping into the Championship.
