Poyet disappointed by second half performance
Adam Johnson put Sunderland ahead after a goalkeeping error from Hugo Lloris, before Paulinho levelled matters going into half-time.
John O'Shea guided the ball into his own net five minutes into the second half and the hosts failed to find a way back into the match.
The result leaves Sunderland bottom of the Premier League, five points adrift of safety, and Poyet was at a loss to explain where the match went awry for his side.
"It's difficult to analyse the game," he told the club's official website. "We conceded maybe at the wrong time, but then the second half, it was very disappointing.
"Things happen in football and you never know the consequences. It's a totally different game if you come in at half-time 1-0.
"Saying that, we talked about things at half time - we needed to go out second half and perform, we're playing against a very good team, and somehow again we conceded an own goal.
"Then it was too open and a game that I don't like to play.
"When you play against a better team you take too many risks, too many chances."
But Poyet could draw some positives, particularly from the Johnson goal that put the men from the Stadium of Light ahead.
He added: "That's the way I would like this team to play football, but I've said it a few times and I'm going to repeat it again now - we cannot do it for long periods, we cannot maintain that level. Either because of the concentration or the quality.
"Nobody can say that we are not trying and the players are trying their best, but the table is there and the table doesn't lie.
"Other teams, they win somehow - we don't. Every single game is bigger than the one before."