He was one of the best players on the pitch, even though he did not record assist or a goal, which is really something considering he has been involved in just four goals since the start of last season.
"We lost so many balls in midfield", Mourinho told BT Sport.
Shaw drilled a shot wide of the far post off a 61st minute corner kick as United began to reassert its control of the match.
Pogba had a rather disappointing performance at the heart of the midfield in the South of the Coast and he appeared disinterested for the vast periods of the opening period of the game.
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Mourinho's side did nearly take an early lead through Lukaku, but looked ragged down the other end and, after missing several chances to clear their lines, Southampton's Michael Obafemi laid the ball off for Armstrong to break the deadlock.
Manchester United may have underperformed in recent weeks at Old Trafford but they have shown an upsurge in form on their travels, beating Juventus in the Champions League, drawing with Chelsea and beating Bournemouth, who are a much better team than their opponents this weekend, in the last month.
"That was hard to have that continuity".
"With all the respect, we don't have many mad dogs that bite the ball and press all the time we don't have many people with that spirit".
Mourinho lauded Nemanja Matic and Scott McTominay but was critical about the rest of his midfield. "Only centre-back we have available to play is Phil [Jones]".
Pogba has reportedly told his former team-mates at Juventus he wants a return to the Old Lady, while he also said Turin feels like home, and it could be the cards if his relationship with Mourinho doesn't improve.