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.
"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.
"The linesman did something we were not expecting. Sometimes these things go for you, here it went against us. If you want an excuse, you get one."
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- Aston Villa