The 18-year-old defender played a full 90 minutes as Spurs hammered Gillingham 5-0 in the third round of the EFL Cup.
After the match, academy product Carter-Vickers admitted it was a significant moment in his career to make his bow for the North London club.
"It's a dream come true," he told Spurs TV.
"I've been working hard all these years and to get to this stage, to play and win 5-0, it's a dream.
"Obviously I was a little bit nervous but I think that helped me. It keeps me on my toes."
The USA U23 international was also close to scoring early on when he headed just wide from an Erik Lamela corner.
He added: "We've been working on the corners in training and to get an opportunity in the first five minutes was good.
"I'll keep my head down and keep working on the training ground and just push on."