The 19-year-old, who joined United from Southampton for around £27m earlier this year, has made just three Premier League starts after missing the start of the season through injury.
In the first half of last night's 2-2 draw at West Bromwich Albion, Shaw made no tackles, clearances or interceptions and lost possession nine times.
"They haven't seen the best of me yet," PA quotes Shaw as saying. "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."
Shaw is the club's number-one option at left-back following the departure of Patrice Evra in the summer.