During the Premier League era, 13 titles have headed to Old Trafford.
Sir Alex Ferguson landed all of those crowns and there has been a humbling process of rebuilding since his departure in 2013.
Mourinho is the latest to take on that challenge, but he is struggling to replicate successes of the past and currently has his side sat seventh in the English top-flight table.
He will be hoping to become upwardly mobile when visiting Southampton on Saturday, but Targett says the Saints are confident of piling more pressure on the Portuguese coach.
“The fear factor has definitely gone,” he said ahead of a clash with United at St Mary’s Stadium.
“You can see how United have played recently. They have still got unbelievable talent but defensively I think they have problems.
“It is a big game. They are struggling. It is not like the old Manchester United. We can get at them and hopefully we can start turning things around.
“Any home game, you have to be positive. We haven’t done that enough this season.
“It will be a good chance to start on Saturday. It would do us the world of good and get the fans back on our side.”
Targett is right to suggest that United have struggled at the back this season, with 21 goals conceded in just 13 games.
Mourinho’s side have kept just five clean sheets across all competitions, with only two of those secured in the Premier League.