Shaw has been one of the top performers for Manchester United this season and is regularly trusted by Ole Gunnar Solskjaer.
The England left-back has been coping with criticism since joining Manchester United in 2014 due to his fitness and inconsistent performances, but his performances have gone up to the next level this season.
The defender did struggle under the management of Jose Mourinho and admitted that it was a hard time for him at Old Trafford.
But he insisted that he always had the belief that he would get the chance to prove himself at Manchester United and show the qualities that prompted the club to sign him from Southampton in 2014.
He also stressed that there is more to come from him in the near future as he continues to learn and improve.
Shaw told the BBC: “It was a very hard time.
“A couple of years back when I wasn’t playing, wasn’t even involved and there were times that people believed that he could leave.
“But like I said, I always believed that I could fight my way back and get into the team and show people what my qualities are.
“I feel like I am starting to do that now but there is still much more time.
“I am still quite young and I have still got time to improve.”
The 25-year-old has featured 26 times for Manchester United this season in all competitions and has five assists to his name.