The Japanese star joined United from Bundesliga side Borussia Dortmund last summer.
The 24-year-old made his first league start under David Moyes against West Brom on Saturday.
“I have to take this like some kind of message (from the manager),” he said.
“I need to improve more and more, or I cannot survive at this club.
“I have to take this in a positive way and keep trying to do my best.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.