Dzeko says sorry for substitution strop
His actions went largely under the radar during Tuesday's Group A match after coach Roberto Mancini disclosed that Dzeko's fellow striker Carlos Tevez had refused to go on as a substitute in a separate incident.
Argentine international Tevez was later suspended by the club pending an investigation into his conduct.
"I know my reaction was bad and I have spoken to the guys and to the coach as well," Dzeko told the club's website on Thursday.
"I have apologised for the reaction and Roberto has accepted it and said that everything is OK and that we have to be positive for the next game [at Blackburn Rovers on Saturday]."
Dzeko joined City from VfL Wolfsburg in January and said he was particularly keen to do well on his return to Germany.
"I was unhappy because we were 2-0 down and I wanted to win the game," he said. "It was something special for me to go back to Germany where I played for a long time.
"Things didn't go well for us. That is why I was extra frustrated."