Manchester United must still work hard in order to turn into a force that can duel and excel in matches against big teams. Despite the fact they have been in a position to earn victories in games against other small teams, the outcome has not been good enough to build confidence and stand in the leagues. The next matches in September will be very important to determine whether or not they can change their ranking. Some people argue that the current manager has failed to provide positive changes as expected, hence the need to employ a manager capable of bringing profound changes to the team and meet the expectations of the fans.
Manchester United cannot be happy with being able to beat Southampton even though with a fairly satisfactory score, It is true what you said they still have to be able to work hard to compete better with other big teams. Their previous victory was not enough to bring them to a profitable point, because they are still in a poor ranking so they have to be able to be better to get a profitable ranking but I don't think it's easy.
Apart from that, Man United fans certainly hope that their proud team can return to its glory again, but indeed their Manager is in the spotlight because he has been labeled as failing to bring Man United better or back to its glory days. I myself think Man United will find it difficult to return to its glory days.