The South Korea international, who joined Atletico from Paris Saint-Germain in late July, came off the bench in the 63rd minute at the Seoul World Cup Stadium, taking a free-kick that flew over Gianluigi Donnarumma's crossbar and forcing a chance inside the box after a pass from Arnau Sola during his 27 minutes on the pitch.
"It's something very special to be able to debut here. Koreans have a lot of affection for me and I also have a lot of affection for my people. I am very happy," Lee said in his post-match press conference, when asked about making his bow in front of his home support.
"We are not so happy about the defeat, but this is only the beginning. Now we will prepare in the best way for the upcoming matches against Marseille and in La Liga to get victories."
Diego Simeone's side had trailed to a goal from teenage defender Jorge Dominguez before Omar Marmoush's second-half brace and a late Rayan Ait-Nouri strike sealed the win for Manchester City in front of around 50,000 supporters.
Lee, who wears the number seven shirt previously worn by club great Antoine Griezmann, said the emotion of representing Atletico for the first time had left a lasting impression.
"I felt very energetic and very happy alongside my team-mates. As I said, this is just the beginning. I am going to give 120 percent for this club, for all the people of Atletico Madrid and for my team-mates," he said, reflecting on what it felt like to wear the red and white for the first time.
Asked about the position he would prefer to play in for his new club, Lee said he was open to featuring wherever Simeone needed him.
"Any position works for me. Wherever I play, I am going to help the team and give 120 percent. I only think about helping the team, which is the most important thing," he said.
Lee's arrival in Seoul had been delayed by administrative issues connected to his military service exemption, causing him to miss Atletico Madrid's earlier pre-season match against Manchester United in Sweden. He is now expected to link up fully with his new team-mates as Atletico's preparations continue ahead of the new La Liga season.