Video on social media appears to show Erling Haaland's dad taunting the home fans before being removed from his box.
Haaland tweeted: "OK. RM was not happy we were celebrating KDB goal.
"Other than that we had to move because RM fans not happy with 1-1."
De Bruyne scored in the 67th minute to cancel out Vinicius Junior's opener.
Haaland waved with both hands while smiling at the crowd below him, cupping his ears to the Real Madrid fans and gesticulating, while reports in Spain suggested he threw food at the supporters.
He tweeted again on Wednesday to say it was "not true" that he had thrown anything.
"We had some good banter with Madrid fans," he added. "They were not happy when City scored. Typical.
"Then we had to move 50 meters away. Nothing more. All happy. Well nearly."
The former Manchester City and Leeds midfielder is a regular at City's matches, where his son has scored 51 goals so far this season.
Spanish giants Madrid have lifted the Champions League trophy - a competition City have yet to win - five times since 2014 and knocked the Premier League champions out of the tournament at the semi-final stage last year.
In October reports suggested that Haaland's contract contains a special release clause for him to join Real Madrid in 2024, which City boss Pep Guardiola later said is "not true".
The 22-year-old's agent, Rafaela Pimenta, said in March that a move to Real Madrid is "the dream" for any player.
City host Real Madrid in the second leg at Etihad Stadium on Wednesday, 17 May.
Victory for Guardiola's side would see them face either Inter Milan or AC Milan in this year's final on Saturday 10 June at Istanbul's Atatürk Olympic Stadium.