Lingard, 25, scored 13 times in all competitions for United during the 2017-18 campaign, and worked his way into the England XI ahead of the 2018 World Cup.
The attacker is again expected to be in the team when England face Colombia in the last-16 stage of the World Cup on Tuesday night, and Carrick has hailed his former teammate.
"I think his movement - he moves off the ball very well. It's something that sounds quite simple, but it's difficult to defend against," Carrick told United's official website.
"He senses where the space is and how to use it. I wouldn't necessarily say he's a dribbler with skills and tricks but he's dynamic. How he plays, he is unique in some ways.
"You don't see so much of that in the game as everyone wants to get on the ball and do something on the ball. Off the ball, he's very effective."
Lingard was on the scoresheet in England's 6-1 win over Panama in the group stages of this summer's competition.