The 20-year-old, who praised the new boss, wants to remain grounded regarding his own chances of success at Old Trafford despite shining in preseason.
Moyes was announced as Ferguson's successor in May and officially took the reins on July 1 before guiding the club on its preseason tour of Asia and Australia.
Lingard, who scored in Tuesday's 3-2 defeat to Yokohama F Marinos, believes the new manager is a like-for-like replacement.
"He's good, he's like a young Sir Alex really," he told reporters. "He's going to learn and get better obviously, he wants to win trophies."
Lingard has now scored three goals in two preseason matches, leading Moyes to suggest that the 20-year-old is on the verge of the United first team, but the player himself is keen to remain grounded.
"I've got to keep playing well, getting my name on the score sheet and keep playing in the rest of the games," he added.
Ryan Giggs also admitted that things are starting to take shape under Moyes' stewardship.
"It's something new for the players," he added. "The players are getting used to the manager, the manager is getting used to the players.
"We've only been together for maybe three weeks, but we're enjoying it, we're enjoying the tour so far and looking forward to the start of the season."