The Black Cats ran out against Aston Villa knowing a victory could lift them out of the drop zone after encouraging results at Everton and Cardiff over Christmas.
However, a 1-0 defeat at the Stadium of Light plunged Poyet's men back into the mire as 2014 got off to the worst possible start.
Clearly angered by what he had just witnessed, the 46-year-old Uruguayan was keen to say as little as possible in public.
In a brief post-match press conference, he said: "It was a very difficult day for me today.
"I need to be careful with what I say because it could bring consequences, so I am going to say very little. Sorry about that, but I think it is best.
"I think you want to see me here every week, so I would prefer to keep it short. There is disappointment of course, I didn't expect that."
The game was settled with just 15 minutes played when Gabriel Agbonlahor, who scored the only goal in a 1-0 win at the Stadium of Light last season, capitalised on Lee Cattermole's error to round goalkeeper Vito Mannone and roll the ball into the empty net.
Sunderland thought they had levelled seven minutes after the restart when Emanuele Giaccherini fired home from Steven Fletcher's knock-down, but a harsh offside flag ended his celebrations.
The home side were otherwise toothless in their attempts to restore parity, and Villa substitute Marc Albrighton was unable to take advantage of either of the two late opportunities with which he was presented to cement victory after Phil Bardsley had cleared Christian Benteke's shot off the line.
Poyet, whose side are now four points adrift of 17th-placed Cardiff, was unhappy with the offside decision, but was in no mood to allow his players to use it as an excuse.
He said: "It could be a good excuse, that the referee [Mike Jones] was poor. He didn't let us play when we needed to, he stopped the game a hundred times, he talked to everybody - the only thing missing was him making a phone call.
"And then the linesman - normally it should be very difficult for a person 50 yards away to see a 5'6" player behind a 6'2" defender. Incredible.
"He probably saw the top of his hand and gave him offside. That is the excuse of the day today.
"The linesman did something we were not expecting. Sometimes these things go for you, today it went against us. If you want an excuse, you get one."
Villa counterpart Paul Lambert admitted he did not have a good view of the incident.
He said: "If it's offside, then it can't be a goal, can it? I couldn't see - it's hard to see from where I'm standing, but the best one in the place to see is probably the linesman."
Lambert was understandably delighted with the result, Villa's first league win in six attempts, as well as the returns of Ron Vlaar and Benteke from injury.
He said: "I thought we deserved it - I thought we could have run out more comfortable winners. We should have at least had three or four, the chances we had.
"Coming up here was always going to be tough because of Sunderland's situation, but I felt the Swansea game gave us a platform to try to build.
"But we are a football club that can't carry big injuries to big players, and I think it was evident today, the two lads coming back gave us a major lift."
Lambert hopes to add to his squad this month, but like Poyet, who declined to comment on the club's pursuit of Brighton duo Liam Bridcutt and Will Buckley, he was giving nothing away.
He said: "If I can, I will, if I can. Yes, there are ones I would like to try to bring in. But if we can, we can; if we don't, then we don't."