The 17-year-old was one of 10 changes made by Enzo Maresca following Sunday's dramatic Manchester derby victory, but he quickly showed why he could have a role to play for the first team this season.
Samba, the son of former Blackburn Rovers and Queens Park Rangers defender Chris Samba, admitted he could hardly believe how his debut unfolded.
"To get a debut like that is mind-blowing. I couldn't believe it myself," Samba said.
"But that's just the beginning, I've got a big career ahead of me. It was a great debut."
Maresca revealed that Samba had been asked to play as a central striker despite having never played the position before.
"I asked him in the last three or four days when I decided to play him as a nine - I asked him if he had played that role and he said he had never played there before," Maresca said.
"He's very good at finishing so I think it was a good game for him."
Samba opened the scoring when he stooped to head in Allan Elias' cross after Norwich goalkeeper Daniel Grimshaw failed to deal with the delivery.
Rayan Cherki doubled City's advantage before Allan marked his first appearance since his move from Palmeiras with an impressive goal.
The Brazilian midfielder picked up the ball, weaved through the Norwich defence and fired into the far corner shortly after half-time.
Samba then added his second with a superb curling finish, punishing more poor defending from the Championship side.
Ryan McAidoo completed the scoring late on as City booked their place in the last 16, where they will face Brighton.
Maresca was delighted with Samba's performance but was careful not to put too much pressure on the teenager.
"He is not a nine for sure but he was good," the City manager said. "He is young, full of energy, he is strong, he can finish and he made some good decisions, some passes to team-mates.
"So I am happy, but again, they are young and we need to go slowly with them."
The victory maintained Maresca's perfect start since taking over at City, with six consecutive wins across three competitions.
The manager also stressed that the young players involved against Norwich are likely to receive further opportunities as the season develops.
"We have different competitions. We have many games," Maresca said. "We are just at the beginning of the season. For sure, the ones that played tonight during the season will play Premier League games and Champions League games as the season is so long."
City return to Premier League action on Sunday when they host Sunderland at the Etihad Stadium.