Regardless of the goal Arsenal scored which I think was just a lucky one, Manchester United played awesomely, they had more ball possession, they has more short on target and they had the overall better performance than Arsenal in that encounter. So for me I don't think there's any special thing Arsenal played to say they wanted to keep a clean sheet from the beginning of the season, they had to stand their feet to protect the only goal they had till the final whistle which made them fall back a lot of times, this was far from the Arsenal of Last season that will be winning a team and still keep them under pressure.
I agree that Manchester United played a better game than Arsenal but how do you call Arsenal's goal a luck? it was their hard work that led to the goal Riccardo Calafiori scored. What you should understand is that Manchester United was playing at Old Trafford so the pressure they gave Arsenal was expected and regardless that they made several attempts but they lacked accuracy and precision even though they got many shots on target. Keeping a clean sheet is a big flex especially to the goalkeeper. For the past 2 seasons Arsenal have conceded the least goals in the Premier League so starting the season with a clean sheet is a good way to go.
It is rather too early to start comparing between Arsenal's last season performance because the league just kicked off and they just played the first match of the season so in subsequent matches they will play better but do not forget that Manchester United isn't also a team to overlook because they added quite some intelligent players to their squad so you don't expect Arsenal to outperform them easily.