The talented 18-year-old burst onto the Old Trafford scene this season after being handed his chance to impress by manager David Moyes.
Januzaj signed a new five-year contract with the current champions in October and has set his sights on silverware and success over the long-term with the Red Devils.
"You always have to keep going and work hard if you want to be even better. My parents always told me to keep my feet on the ground, keep working and, if you can, try to be the best player in the world," he told MUTV.
"In football it's not [about] age. If you're good enough to play, you have to play.
"I think the boss gave me the chance because he's known for giving a chance to young players. He's a top manager and knows exactly what he is doing with the players and everything else.
"My first opinion was to sign for Manchester United - that was my first choice. Now I've signed for them and I'm happy here. If I could play all my life at Manchester United, I would do it for the club.
"Winning trophies is the only thing I want and to try to be the best player."
Januzaj's full Premier League debut came against Sunderland in October when he hit the headlines with two goals in seven second-half minutes to secure a vital victory for United.
"I think, to score two goals on my debut, I can't ask for any better," he added.
"I was really happy with those two goals and now have to continue to score more if I can. That was my first game, giving me the chance to play, and I had to prove I could play at first-team level.
"You don't really have a private life anymore. You have to sacrifice yourself and so it's not that easy."