In my opinion it was a very poor performance, A team that wants to win the Premier League wouldn’t play the way Arsenal played against Manchester United. And they were just lucky not to have conceded against Manchester United, Manchester United was the better team in the game, well the season is too early for Arsenal to score a goal and start defending their one goal advantage, I think this was one of the reasons they lost the premier league in previous seasons, now the difference between Arsenal and Liverpool and Manchester City is they will not sit back and defend they will go all out to score another goal instead of sitting back to defend, Liverpool was far better than Arsenal last season and that is why they have so many points advantage against them last season, If Arsenal continue to play this way they will not be able to win the league, because they will have to meet so many teams that plays a low blocks. Arsenal played so many draws last season because of playing this defensive style of football.
I wouldn't necessarily say that the performance of arsenal against Manchester united was a poor performance because the goal was to secure the desired three points, not a fancy performance as most folks out there expected it to be, yes it's actually true that they can't play like that against a smaller opposition because they must come out attacking if they want the whole three points, but that's by the way.
This season I wouldn't be judging any of the top teams just yet because in the first round of matches, not all of the top side met a top team, the opponent of arsenal and Chelsea are way more stronger than the opposition of Manchester city and that of Liverpool, so after the first five games, that's when I can say that this or that team is better than this one or that one.