Since making his first-team debut in August's Community Shield victory, the youngster has become a regular under the former Everton boss this season, scoring twice in 10 Premier League games.
|MAN UNITED LATEST
|7/1||Manchester United are 7/1 with BetVictor to win the FA Cup|
"He will win trophies," the 18-year-old told MUTV.
"Don't forget, it is a new coach. Everything is new. You have to give it time.
"I think he is a good coach. All the players are ready to work hard as well and everything will come."
Januzaj, who arrived at United in 2011 after spending time in the FC Brussels and Anderlecht academies in his native Belgium, says that wants to stay at Old Trafford for "a long time".
"I am happy here," he enthused. "When I moved to Manchester I wanted to play with the first team. Now I want to stay here, play for a long time, if I can, and be the best player I can be."