The Citizens entered the contest in Serbia having already qualified for the last 16 as Group G winners, so Guardiola opted to make nine changes to his starting lineup and handed academy graduate Hamilton his full debut.
Hamilton, who joined City's academy at the age of nine, marked his memorable night with a powerful strike from a tight angle to open the scoring in the 19th minute.
At the age of 20 years and 30 days, Hamilton has become the youngest player to score on his Champions League debut for Man City as well as the youngest Englishman to score on his debut in the competition since Manchester United's Marcus Rashford (19 years and 316 days) in 2017.
Guardiola was delighted for Hamilton, who first came across the Catalan boss when he was a ballboy during Man City home encounter with Crystal Palace in 2017.
During his post-match press conference, Guardiola was left surprised after being shown footage of himself interacting with Hamilton as a ballboy on the touchline at the Etihad Stadium.
"I didn't know this. Six years ago? Wow yeah, here you are," said Guardiola. "What a goal and what a game.
"I am so happy for him. He is training well and we saw his skills. He made a fantastic goal. Defensively he was aggressive. Congratulations to our academy for how many players came up and how many we sell."
City's win over Red Star was a special night for the club's academy as Hamilton's opener was followed by Oscar Bobb's first senior goal, with the Norwegian later receiving the man-of-the-match award.
Midfielder Mahamadou Sissoho came on as a second-half substitute to make his first senior appearance, and fellow academy graduates Rico Lewis and Phil Foden were also involved in the win over Red Star, while goalkeeper True Grant and defender Max Alleyne also travelled with the first-team squad to Serbia.
Commending the conveyor belt of talent that has emerged from City's academy during his time at the club, Guardiola said: "It's not easy to get opportunities at that level because in big clubs you don't wait.
"In the end we wanted to put Max on but the game was not under control.
"It's a compliment to the academy. Cole Palmer was here. Romeo Lavia, James Trafford, [Gavin] Bazunu.
"Many players in our academy are in the Premier League or Championship. They have done unbelievable. It is top class."
Man City, whose victory over Red Star has seen them break a Champions League record, will now turn their attention to Saturday's Premier League clash with Crystal Palace at the Etihad.