The Scot failed to win a trophy in his 11 years at Everton and faces the pressure of succeeding Sir Alex Ferguson, who won 13 Premier League titles along with two Champions League trophies in his 26 years at the club.
Moyes told reporters: "You have to do well in all competitions — not just the Premier League.
"When you are at Manchester United, my thinking is you have to go for everything, you attempt to win everything. Maybe you miss out sometimes, but you have to try to win all the trophies.
"I've done it everywhere else I've been and I'll certainly do it here because I have a bigger squad, quality players and a club with the tradition of being used to winning things."
Moyes has won just one trophy in his entire managerial career - the Division Two title with Preston North End in 2000.