Shaw moved to Old Trafford from Southampton in the close-season, but suffered a difficult start to his time at the club after new manager Louis van Gaal criticised his fitness.
The 19-year-old made his debut in last month's 2-1 Premier League win over West Ham, and is looking to stake a claim for making the left-back position his own.
The high-profile arrivals of Angel di Maria and Radamel Falcao dominated the headlines during the recent transfer window, and Southgate believes Shaw can only learn from training with players of that quality.
"I think what he now has is a recognition of what 'world class' looks like," he said.
"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.
"He was able to share those stories among our lads in the Under-21s because all players at times in their careers think they are nearly there - and then you discover you still have a bit of a way to go.
"You continually have to strive to be better than you are and Luke realises that now."
