Paul Pogba apologised for the "stupid mistake" that cost Manchester United and helped Arsenal end their 29-match winless Premier League run away to big-six sides.
Ole Gunnar Solskjaer's 100th match at the wheel ended in a disappointing defeat at Old Trafford, where the Red Devils started a top-flight league season with four winless matches for the first time since 1972-73.
United were a shell of the side that hammered RB Leipzig in the Champions League and Mikel Arteta's Arsenal punished them, with Pierre-Emerick Aubameyang's spot-kick sealing a 1-0 win on Sunday.
It was the Gunners' first league win at Old Trafford since 2006 – and first at a big-six rival since January 2015 – and gifted to them by Pogba's needless penalty-box challenge on Hector Bellerin.
"We know it's a poor performance," the midfielder told the BBC. "Myself, I cannot give a foul away like this.
"I thought I would touch the ball but I didn't. (I) cost us the goal today with the penalty.
"Like I say, details. We have to do better, the team, myself, it starts with me.
"I felt like I touched him a bit, I knew I was in the box, I shouldn't have given a penalty away like that.
"Maybe I was a bit out of breath, it made me do this stupid mistake. I will learn from that, I'm not the best defensively in the box, I can work on that."
Solskjaer echoed Pogba's view after a match that looked set for a 0-0 draw, just like last weekend's clash with Chelsea.
"Paul knows if he stays on his feet and he shuffles the boy… because he was on his way out of the box, it's a soft pen to give away," he said. "Those things happen.
"I know he touched him enough to give away a pen and that went against us. Paul held his hand up and he knows he could and should have done better in that instance.
"That was the difference between the teams today. It always looked like a 0-0 to me."
Roy Keane was watching from the stands as part of his role as a Sky Sports pundit and was far from impressed by his former club's performance, saying he did not "see guys you want to be in the trenches with, guys you trust".
When those comments were put to Solskjaer, the United boss said: "Well, in the first half there were no tackles, no fighting, you have got to create atmosphere yourself.
"These games against Arsenal were always fierce, tackles flying.
"We didn't have the tempo or intensity for that, absolutely, and I was disappointed with the first-half performance.
"In the second half we were better. Unfortunately, they got the penalty and we just couldn't produce the response."
While United were left ruing what could have been, Arsenal were celebrating what manager Arteta believes is a key moment in their progression.
"Obviously there is many factors for us and it's not a coincidence," he said after the Gunners ended their 29-match wait for a league win at a big-six rival.
"We have to change that (record) dramatically and very quickly if we want to be fighting to be a top team because if not we're never going to gain the consistency required at that level.
"It's great, big belief for the players and belief when we go somewhere else.
"To be fair, this season we went to Anfield and played them face-to-face, we went to the Etihad and we did not deserve to lose the game.
"We come here again and did the same, but this time we win."