United's Marcus Rashford scored the first goal of the game for the Red Devils in the 27th minute but the Gunners swung into action after conceding.
Martin Odegaard equalized for Arsenal one minute later, Declan Rice gave them the lead in the 96th minute and Gabriel Jesus made it 3-1 five minutes later.
“I think we played (a) very good game. But everything went against us and then, of course, then you don't win the game and if (we had) a little bit more luck you win the game.
“You saw the game but it's no offside (for the Garnacho goal which was ruled out), wrong angle. It's a penalty (on Rasmus) Hojlund then we concede a goal (scored by Declan Rice) when there's a foul on Johnny Evans.
“(The Declan Rice goal) is offside so you have to accept it but I see the angle. I don't see (it) as offside. No (I have not sought clarification from officials) but that doesn't change the result.”
Manchester United sits 11th on the Premier League table with six points from four games.
They play Brighton and Hove Albion next on Saturday, September 16 at Old Trafford.