Ole Gunnar Solskjaer speaking to BBC's Match of the Day: "That's football for you. It goes up and down.
"We didn't turn up, especially in the first half. That's what we have to address because we know these boys can be so good.
"We knew that this was the big game this week. And unfortunately in the first half we didn't play well enough.
"Second half we played better, we never seemed to have to defend too much. But when we did have to, we were too slow and gave away the penalty."
"The boy is running away from goal, there is no need to go for the ball. Not much of a touch, but it's probably a penalty.
"It's for other people to judge if we're making progress."
United midfielder Paul Pogba: "We know it's a poor performance. 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."
Arsenal boss Mikel Arteta speaking to Match of the Day: "I wanted to generate belief and I asked them to be who we are as a team right now.
"I'm delighted because we played with a lot of courage and big personality.
"They played a really tricky formation with four midfielders and two that constantly strain your back four. We could have scored twice in the first half and when we scored the goal we had to manage those moments. There was high stress, it is different to any other ground.
"Individually you have to win the fights and step up to the occasion and the performance of every player today was top drawer."