All eyes were on Poyet's men at the Stadium of Light as they attempted to bounce back from last week's 8-0 humbling at Southampton.
But mistakes proved their undoing again as Wes Brown and Vito Mannone gifted Alexis Sanchez a match-winning double.
Poyet was pleased with his players' efforts on the whole, but rued their defensive lapses.
He said: "It's difficult to analyse the game because the commitment, fight, desire and organisation were there compared to last week.
"But we forgot to leave the mistakes in the dressing room. There is a little bit of anger in the dressing room now."
Poyet also pinpointed Sunderland's failure to impose themselves in the final third.
He added: "If we had cut the mistakes out and done more in the final third, maybe we would be talking about something different.
"I don't want to accept the mistakes but I have to."
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