Manchester United played well and won. Manchester United secured 3 points for the first time this season. This is definitely commendable. Especially the performance of Manchester United's attacking players was very good. Manchester United's players were able to attack a lot. Although we did not see a good performance from Cunha, Mbeumo, Dalot and Bruno performed well.
Manchester United's attacking performance is gradually improving. Against Arsenal, we saw that United's boys were able to attack a lot. However, United's biggest weakness is their defense and goalkeeper. In this match, Burnley's players only had 6 shots. Out of these, 3 shots were on target. And United conceded two goals. Burnley's players could not attack much. Even then, the team scored two goals against Manchester United. This highlights the weaknesses of Manchester United's defense quite well. Amorim needs to work more on Manchester United's defense.
Yes, it's fair to say this wasn't a beautiful victory for Man United, as they earned it with great difficulty until the final minute. Man United performance has improved, especially in attack but as you said their weakness lies in defense. This is perhaps something Amorim should focus on to make their defense more solid and strong going forward. It wasn't a beautiful victory, but it was an important one for Man United.
This first victory could motivate Man United even more and could be a boost for Man United in their upcoming matches. A win will restore their confidence especially if it's a hard won victory. There were some positive developments in that match Mbeumo scored, Bruno converted a penalty, and Dalot provided an assist. Hopefully these players will do the same in their next matches.