The Black Cats saw their recent Barclays Premier League recovery stall on Saturday as they went down 2-0 to the Tigers at the Stadium of Light after central defender Wes Brown was dismissed with less than four minutes played.
It was all painfully reminiscent of Poyet's third game in charge when he sent his side into battle at the KC Stadium on November 2 and saw both Lee Cattermole and Andrea Dossena sent off before half-time as Carlos Cuellar's own goal handed the home side victory.
The 46-year-old said: "It wasn't to be. It was one of those days when it doesn't matter how you play or what you do because something will happen and go against you.
"I'm very pleased that we don't play Hull any more this season because every time we play them, something happens."
Brown's premature exit proved to be the pivotal moment in a game which slipped from his side's grasp before it had really begun.
Phil Bardsley's poor back pass put Shane Long in on goal and the former Manchester United defender's efforts to rectify the damage resulted in a sliding challenge which sent the £7million January signing sprawling.
Referee Mike Jones had little option but to show Brown a red card - his third of the season, although one was later rescinded on appeal - but Sunderland were at least spared further punishment as the offence was committed marginally outside the penalty area.
Poyet later admitted it might have been better to allow Long to go on and shoot, but did not blame his player for his illegal intervention.
He said: "It was a little bit of bad play plus a decision. In modern football now, sometimes I don't know if it is better to allow the opposition player to have a shot.
"We would be losing 1-0, but it would be 11 v 11 with 87 minutes to play.
"It's easy to say; it's very difficult to do it when you are on the pitch and you are trying to stop the opposition from scoring, so I have nothing to say to Wes.
"He did what was needed at that time. Unfortunately, it was late and it was a sending-off."
The Black Cats' woes increased with 16 minutes gone when Long headed them in front, and their misery was complete 17 minutes after the restart when fellow new boy Nikica Jelavic scored his first goal for the club after Maynor Figueroa's long-range attempt looped up nicely for him off defender Santiago Vergini.
Sunderland, who have spent much of the season to date anchored inside the bottom three, had started the day in 14th place, but ended it in 17th and just a point clear of the drop zone.
They head for title challengers Manchester City on Wednesday evening knowing they cannot afford another off day if they are to stand any chance of returning with a positive result.
However, Poyet for one will not be reading too much into Saturday's performance and result.
He said: "We can talk about how (Hull) planned the game or how they wanted to play, but at the end of the day, they won the game because Wes Brown got sent off, that's the bottom line.
"For five or six games, they couldn't win before this one, so something went for them.
"That can happen on Wednesday, it can happen in two weeks' time for us, I suppose. It's not always against."
Opposite number Steve Bruce left Wearside a much happier man than when he last did so having been shown the door by Sunderland in November 2011.
Bruce was particularly pleased with his front two, but midfielder Livermore, on loan for the season from Tottenham, was equally impressive.
He said: "I thought he was outstanding. He's been a terrific loan signing for us, a terrific loan signing.
"We will do our utmost to make it permanent if we can, but obviously we have got to stay in this division first, if that's possible."