Jermain Defoe's wonderful left-footed volley on the stroke of half-time gave Sunderland a fifth consecutive Tyne-Wear derby win.
Carver, in charge of Newcastle until the end of the season, was angered by his side's showing but refused to criticise his defence and goalkeeper Tim Krul.
"The way we performed first half, we were abysmal. I'm not saying we didn't give 100 per cent but we were poor," Carver told Sky Sports.
"It was a world-class strike on Jermain Defoe's weaker foot but if we had gone in at half-time goalless we'd have been delighted because we were second best.
"We huffed and puffed [in the second half] but it wasn't good enough. We were so negative, every day we go onto the training ground and I'm most positive person.
"I don't put shackles on players, I want players to be exciting because I've been around exciting teams.
"Without going into it much, the back four is a makeshift back four and they stuck by their jobs along with the goalkeeper.
"They deserve credit but the other units I'm not happy with."
Krul was spotted congratulating Defoe on his strike at half-time, with Carver pressed on whether such a gesture was wise in the midst of a fiercely contested derby.
"If there's one guy who cares about this club it's Tim Krul, whenever we're not happy or we have issues he's always the guy to deal with it and he acts like a captain," the Newcastle boss added.
"Give me Tim Krul any day because he is Newcastle United crazy and if that has gone on, then it happens. We get slaughtered when were not sportsmanlike.
"When you see skill, you have to accept it."
