Shaw has made two appearances for the Red Devils since joining the club from Southampton in the summer, and played 71 minutes in the recent 2-1 win over Everton.
And Southgate believes that playing alonside the likes of Falcao and club-record signing Angel Di Maria has taught the 19-year-old what it takes to really be considered “world class”.
“I think what he now has is a recognition of what ‘world class’ looks like,” Southgate told the Mirror.
“He might have had an idea of what he thought it was before, but training at Manchester United with the likes of Radamel Falcao and Angel di Maria has given him a full understanding of the concept now.
“He would have known there was a level, but now he knows there is a level above that.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news