An Olivier Giroud double put Arsenal 2-0 up at half-time, with both of his goals coming as a result of poor defending from set-pieces.
Moussa Sissoko pulled one back in the 48th minute for Newcastle, who were left to settle for a valiant defeat despite piling pressure on Arsenal in a frantic second half.
"I'm exhausted to be honest. I think I've kicked every ball," Carver said in quotes reported by Sky Sports.
"What I will say is, what a fantastic performance by the 11 boys, plus Jonas Gutierrez coming on, and giving a performance like that. I'm so proud of them.
"We've scored an Arsenal-type goal, haven't we? Great build-up play down the right-hand side, a cut back and what a finish by Moussa Sissoko.
"What is disappointing is the type of goals we've conceded. Two from set plays - they haven't opened us up.
"I thought we started the game quite well. There wasn't much in it. We had a nice shape to the team and there weren't any problems, and that's why it’s a little bit frustrating.
"When you concede so many laterals eventually you're going to get punished, and we did."
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