We know Southampton is a promoted team that Manchester United should have won easily but the fact that it happened and it was really easy for him, it doesn't matter what matters is that fans are happy Erik Ten Hag will have no more pressure.
Next week with Crystal Palace that team could be a surprise at home, while Manchester United must be wary of the opponent I'm sure if they struggle then this could be another defeat, but we don't know yet how the Red Devils performance is difficult to guess.
They have not been able to be consistent, maybe Erik Ten Hag is still fixing all the tactics and the squad he plays with.
The comparison of strengths that are quite different makes Manchester United quite comfortable in this match, especially as you say that for now Southampton is still a promotion club, although it cannot be denied that they are not a new name for the EPL but still they are still not able to compete in the EPL it seems.
A pretty good score was shown by Manchester United in this week's match and it is this kind of form that they must maintain because after all at this time Ten Hag is still very much in demand to improve their performance and 3 points is the evidence they must show in each of their weeks considering the diminishing confidence for Ten Hag makes this a little more difficult for them.
With this result at least they stopped 2 consecutive defeats in the previous 2 weeks and of course this is a good motivation for them to be able to develop their performance at this level in the next week.