Sancho had struggled to make an impression since his £73million move from Borussia Dortmund in the summer – with a player who had 54 goals and 67 assists in four seasons in Germany having none in either category in his first 15 United appearances.
But that changed on Tuesday night in Villarreal as the 21-year-old crashed a shot in off the underside of the crossbar in the last minute of the 90 to give United a 2-0 win and confirm their place in the last 16 of the Champions League.
Carrick said it had been important to give Sancho time to settle following his summer move, but there is no doubt about the England forward’s potential.
“As a player sometimes it takes a bit of time to adapt,” Carrick said. “As a younger player coming to such a big club and a new league it’s not easy just to hit the ground running. We were well aware of that.
“Of course we believe in him. The potential he has got is massive. If he can keep doing the right things and keeps himself on the right track he’s got a great chance.
“I’m not surprised by what he did the other night. I’ve seen it in training. I’ve seen the spring in his step, and in his body language. There’s a little spark and hopefully that spark gets bigger.”
Tuesday was arguably Sancho’s best performance in a United shirt, not just for his goal but also for his work rate going in both directions – something that could be a major factor under incoming coach Ralf Rangnick given his intensive style.
“He’s never happier than when he has the ball at his feet and he’s trying to create things and go at the defender,” Carrick said.
“But the biggest thing the other night was the other side of his game, the attitude and work-rate and mentality. I thought he put in a whole performance the other night.
“He’s got a massive future ahead of him if he does the right things with the right attitude.”
Taking charge of his first game as caretaker, Carrick made a major statement on Tuesday night as he handed a rare start to Donny van de Beek, all but frozen out under Ole Gunnar Solskjaer, as Bruno Fernandes began the night on the bench.
United looked ordinary for much of the night until Fernandes and Marcus Rashford came on to replace Van de Beek and Anthony Martial, but the Dutchman will hope he gets more chances now that Solskjaer has gone.
Carrick believes there are several ways the 24-year-old can fit into the side.
“I think Donny is one of those players, because he’s so flexible and he can play different positions – he did that at Ajax and he’s done that for Holland as well – his variety can be a real strength,” Carrick said.
“Obviously we’ve got ideas where we think Donny is most suited but he’s so flexible, so adaptable, there’s two or three positions around midfield where he can play. You could argue he played a false nine at times with Ajax.
“Him being so flexible is a real strength and a credit to what he can bring to the team.”