Rashford started and scored in both of England's matches during the recent international break, but he has been named in the starting XI just once for United so far this season.
The 20-year-old will also miss the next three games due to suspension but, amid suggestions that the striker needs to be playing more regular first-team football, Southgate is confident that Mourinho holds the youngster in high regard.
"It's not my business to interfere with club managers. They have a difficult job to do and they have big squads at the top six, with huge competition for places," he told reporters.
"Jose thinks the world of Marcus. He's a huge admirer of him, but he has got his job to do. There is huge competition for places at his club so you can understand that. I understand the difficulties that club managers have. They have to try and win matches. They have to rotate their squads.
"We really wanted to make Marcus feel important over this period. It was important especially to get him in the penalty box and remembering the areas he needs to be scoring goals from. His confidence will be boosted I'm sure, with two goals against top-quality opposition."
Rashford's last three goals have now all come for England.