Crystal Palace manager Roy Hodgson: "Unfortunately we were playing against a team with so much technical ability. You have got to work so very hard to keep them at bay.
"The first goal was just a fantastic pass, control and shot.
Manchester United boss Ole Gunnar Solskjaer told BBC Sport: "It's always difficult to play Brighton. We have had good results and we've had to earn them the hard way - we managed to find a way in the second half.
Solskjaer told BBC Sport: "Of course it's a concern.
"When you have three clean sheets in a row, that will help you win games - but we haven't produced the quality.
"We just have to find a spark again, the quality again and try to win the games.
Manchester United manager Ole Gunnar Solskjaer : "We deserved to win the game but that is football for you, you have to take your chances and cannot concede with every shot.
"First half I did not feel we played particularly well but scored two fantastic goals, you go in at the break 2-0 up feeling we have not hit where we could do.
Arsenal boss Mikel Arteta: "I thought it was a fair result. Both managers probably think we should have won it.
"Three of our best players were out and that probably has an impact but I'm really happy with the players.
Manchester United manager Solskjaer said: "They are a good side and they have some injury problems but we didn't pounce on that.
"I felt we grew into the game and got stronger and stronger and were closer to winning.
Manchester United manager Ole Gunnar Solskjaer to BBC Sport: "I'm very pleased of course. Any time you get three points you are happy. We had to dig in and earn it and we did.
"Patience and having more composure was the key.
Manchester United manager Ole Gunnar Solskjaer told BBC Sport: "You are always delighted with three points. The performance was good and we created chances.
"It was maybe a little too open and we wasted chances.
Manchester United boss Ole Gunnar Solskjaer said he is not willing to consider talk of a title challenge until after 30 games.
"There's no title race after 15 games," he said.
"You can lose the chance of being in the race in the first 10 games of course but play another 15 and get to 30 maybe, then we can start talking about it when we've at least played more than half the season.
Leicester City manager Rodgers, speaking to BBC Sport: "We showed the mentality to come back. I thought some of our attacking play was very good. You are playing against a team that is so quick on the counter-attack but I felt we counter-pressed very well.