Speaking to BBC Radio 5 Live, the 17-year-old said he had sensed an opportunity was coming in the build-up to the match.
"Right before the game yesterday, the day before — I knew there would be an opportunity to get some minutes for the first time with the first team — to get a debut like that is mind blowing," Samba said.
"I couldn't believe it myself, but that's just the beginning, I've got a big career ahead of me. It was a great debut."
Samba, the son of former Blackburn Rovers defender Christopher Samba, said he had tried not to let the occasion overwhelm him, focusing instead on adapting quickly to the physical step up from academy football.
"I couldn't be happier right now, being my first senior debut, you have to expect everything to go well, the intensity, the level of players, everything goes up and you have to be able to match it and cope with it, and I think I did well with that," he said. "Coming from the 21s to first-team training, that's a big jump — the sessions are more tiring, you have to run more — they demand more of you and you have to cope with it."
The teenager credited the senior squad for putting him at ease before kick-off.
"I spoke to all of them [the first team players], they've all been brilliant with me — before the game, giving me advice — play your game, be you — those words gave me confidence and helped me score those two goals today," he said.
With little time to celebrate, Samba's focus quickly turned to recovery and Manchester City's next assignment.
"I can't wait — recover now, rest, the team goes again — training tomorrow and then Sunderland on the weekend — everyone has to be prepared for that," he said.