Dzeko fired four goals past Tottenham at White Hart Lane in a remarkable performance that left City 5-1 winners over their former fierce rivals for Champions League football.
He found it difficult to adapt after arriving in January from Bundesliga side Wolfsburg, but Mancini said: “We played a really good game, because Tottenham are a fantastic team.
“I was always sure that Dzeko would score a lot of goals for us. He always scored for Wolfsburg in everything that he played for. He was perfect, he was incredible.”
Dzeko, who hit the ground running with a goal in the Community Shield at Wembley, has scored six in three Premier League matches, better than his haul in five months last season.
City’s title credentials were improved by their second successive away win, but City’s manager added: “I think that the season is very long, but it was important that we started well.
“Today, I’m disappointed only for the goal that we conceded. We need to pay more attention in these situations.”
City’s hard-to-please boss was happy to see Dzeko walk away with the match ball but was already thinking ahead with an international week next on the schedule.
He said: “Now it is the internationals, and for ten days we can’t see all the players. The next game against Wigan will be very hard, because now everybody will expect us to win by four or five!”