Mourinho claims that Antonio Valencia is set to be the new club captain, after wearing the armband for most of last season in Carrick's absence.
After Sanchez's move to United, Martial has failed to score a goal, and has dropped behind Marcus Rashford in the pecking order.
The match at Levi's Stadium in Santa Clara, California, pitted a United side playing its second match of the pre-season against an Earthquakes team in the midst of what has been a lackluster Major League Soccer campaign.
'However I can tell you that without the unconditional support of the fans, Anthony would already have asked to leave Manchester United.
Mourinho confirmed the 25-year-old, who has often been criticised for his performances since arriving from Juventus in 2016, will miss the start of the season while he recovers from his exertions this summer. Do YOU think he's good enough to be a regular for Man Utd this season?
Signed from relegated Stoke City, Grant got down well to deny America in the 27th minute as the Mexican side enjoyed a good spell as Roger Martinez bulldozed his way through United's defence and forced the veteran into another save seven minutes later. "I am confident with them because they are all incredible players and Anthony looks very sharp".
There was also space for youngsters Tahith Chong, 18, and James Garner, 17 in the line-up.
Manchester United are now in full pre-season swing, with their tour of the United States of America bringing in record numbers as the juggernaut marches on before the 2018/19 season begins.
After taking on San Jose, the level of opposition goes up a few notches, with games against AC Milan, Liverpool, Real Madrid and Barcelona.
"Of course physically he has his limitations, and when he has one more touch and he allows that body contact of course he loses it, but when he makes the ball move and attacks people one against one, he has quality".
The Chilean forward is experiencing his first pre-season since 2013 after the South American nation did not progress to the just concluded 2018 FIFA World Cup in Russian Federation, but must now increase his training regimes to be in shape ahead of Manchester United's Premier League opener against Leicester City at the King Power Stadium on Friday August 10.
'I would like to play (United's opening Premier League fixture) against Leicester on Sunday, but I have to play on Friday.