The 28-year-old forward's Juve contract expired this summer and he had been touted for a move to Serie A runners-up Inter Milan, which would have ensured Champions League football next season.
The Portuguese coach extended his perfect record in European finals to five titles by guiding Roma to the inaugural Europa Conference League trophy.
Mourinho was booked by referee Mike Dean in the 77th minute after the Portuguese approached the Southampton bench.
Mourinho had to be restrained by stewards when one of Chelsea boss Maurizio Sarri's backroom staff ran in front of the Portuguese to celebrate as the hosts salvaged their unbeaten start
Mourinho appears to have lost his patience with his high-profile star after Pogba urged United to attack more following a 1-1 draw with Wolverhampton Wanderers at the weekend.
United, under manager Jose Mourinho, are seventh in the Premier League after a disappointing start to the season, eight points behind leaders Liverpool and six behind reigning champions Man City.
A downbeat Mourinho on Tuesday refused to comment when asked if he was confident of winning the Premier League title this week.
England assistant manager Steve Holland says Gareth Southgate qualities echo Jose Mourinho, Antonio Conte
Steve Holland worked with the London club's first team from 2011 before joining Gareth Southgate, and England, in 2016.
Mourinho said favourites Brazil and Germany had the most balanced squads and he did not expect the World Cup to see a shock winner in Russia.
Manchester United vs Chelsea: Stakes raised for Jose Mourinho-Antonio Conte feud in FA Cup final showdown
Mourinho and Conte renew hostilities with the stakes heightened when Manchester United and Chelsea face off in FA Cup final.
Mourinho has had repeated run-ins with Wenger during his time in England, notably as manager of Arsenal's London rivals Chelsea.
Mourinho has played down concerns over Marcus Rashford's lack of game time for Manchester United as the World Cup looms.
Lukaku broke his barren run against top six Premier League opposition and provided the winner for Jesse Lingard as Manchester United came from behind to beat Chelsea 2-1.
Liverpool is in prime position to pounce, hosting West Ham after a 10-day break following the 5-0 demolition of Porto.
The midfielder has endured a frustrating spell in recent weeks, having been substituted twice and absent from the starting line-up three times in United's past five games.
Manchester United gaffer Jose Mourinho was irritated at the focus on the absence of Pogba from his starting line-up.
Manchester United gaffer Jose Mourinho hails Scott McTominay after leaving out Paul Pogba for Sevilla draw
Pogba had been left out of the starting line-up for the goalless draw with Mourinho apparently unhappy after the French star withdrew from last weekend's FA Cup win at Huddersfield Town.
Champions League: Manchester United gaffer Jose Mourinho admits concern at Ander Herrera injury in Sevilla draw
Mourinho fears Herrera has a bad injury after the Spanish midfielder was forced off in the first half against Sevilla.
The last-16 Champions League tie against Sevilla marks Manchester United's first appearance beyond the group stage since 2014.
Mourinho played down suggestions that Paul Pogba needs to use the Champions League knockout stage to justify his huge price tag.