The 19-year-old put United ahead after eight minutes of Wednesday's Carabao Cup third-round tie at Old Trafford, cutting inside onto his left foot to score on his first senior start. Mason Mount added a second two minutes later, but Charalampos Kostoulas, Pascal Gross and Maxim De Cuyper turned the game around for Brighton, and Manchester United lost 3-2.
It was the first time in 50 years that they had held a two-goal lead at home and lost.
Lacey's goal came a day after the Mirror reported that another academy prospect, JJ Gabriel, had asked to leave the club. The 15-year-old feels he should already be in the first team after scoring 23 goals in the Under-18 Premier League last season.
Gabriel reportedly flew to Barcelona on Friday for talks, with Real Madrid also interested, but United hope to persuade the forward to stay. Carrick, speaking to MUTV, took the opportunity to remind young players that the club's history of promoting from within has not gone away.
Asked whether Lacey's goal could inspire those in the academy, Carrick said:
"That's it. To have continued moments like that. The history of this club is littered with them. You could go on forever talking about them and that's the magic of it. That's the beauty of it.
"That's why so many people in the academy work so hard and it's what this club has been built upon. So Shea's had that next moment, or the current moment I should say, and we'll see who brings it on to having the next opportunity because we always look forward to the next one."
Carrick also spoke about what the goal meant to the player and those around him.
"It was amazing for Shea and his family and everyone at the academy, connected to the academy, I think to bring Shea through on his journey and to see him start a game at Old Trafford. And for him to do what he does best. I've seen him do that on the pitches outside there [at Carrington] quite a few times and that's his little spot, you know? Getting there and turning on his left foot and coming inside."
He was careful, though, not to let the result overshadow the moment.
"I'm delighted for him. The way the game pans out and the finish of the game and the result, I think it takes it away a little bit but, when the dust settles and he can have a moment, I think he can be very proud of himself because it was a big moment for him."
Lacey could feature again when United travel to Fulham on Sunday.