The 19-year-old left-back arrived at Old Trafford in an estimated £30 million deal from Southampton, but struggles with fitness have limited him to just three appearances.
Shaw's stellar performances at St Mary's Stadium last term earned him a spot in England's World Cup squad, though he was recently dropped to the Under-21 setup.
Despite his stuttering start, Shaw remains confident he will prove his potential with Louis van Gaal's side.
"They haven't seen the best of me yet," he said. "I know I haven't been up to my full potential and I think maybe people can see that at the moment.
"I am trying hard and it's about getting used to everything.
"When you come to a club like this it's never easy for a young player like me.
"But I'll get myself started soon and put in good performances. I wouldn't say I've been horrendous but I know I can do much better. And I need to do better.
"I've come to Manchester United and I know what they need. I've been working hard and the performances will come."
