City's Bosnian striker scored a late winning goal as the defending Premier League champions beat Tottenham Hotspur 2-1 on Sunday to maintain pressure on early-season leaders Manchester United.
Dzeko has now scored 11 league goals coming off the bench and, with Mario Balotelli not even named in City's 18-man squad for the game, his lack of first-team starts indicates the champions' remarkable strength in depth.
"Edin is not happy," said Mancini. "A player who is happy on the bench does not exist.
"We had three important strikers today. Last year we won the championship because of goals from our strikers. Today, we missed some goals from them but hopefully they will continue to score.
"The Premier League season is long and difficult -- there are a lot of teams who can fight for the title. Tottenham can come back and fight for it, as can Arsenal.
"We made some mistakes in the Champions League, but in football you can never say never."
Mancini's assistant David Platt expanded on the role of Dzeko, who previously scored two goals to help City come from behind and win at West Bromwich Albion last month.
"After West Brom, I said then, we can only pick 11 players but hopefully we bring on the right substitutes," said Platt.
"That is the way it's been in the two years I have been here.
"We have a lot of players who could play for most Premier League teams but we can only pick 11 and Edin is one of those players who can either start or be a substitute.
"We needed an injection -- a bit more height, someone to hold the ball up up there, also someone to be a platform.
"Edin has scored some important goals, he's a valued member of our squad. We haven't tagged him 'super sub', if that's what people want to call him."
Balotelli's absence was harder to explain, although Platt backed up Mancini's pre-match explanation that there was no disciplinary issue and the controversial Italian had only been omitted for "football reasons".
"The gaffer can only pick 18 players," said Platt.
"The last time I looked, we were only allowed seven on the bench. He made the decision."
Dzeko's superb finish followed an equaliser from Sergio Aguero that cancelled out a first-half headed goal from Tottenham defender Steven Caulker.
The disappointment for Tottenham manager Andre Villas-Boas was compounded by the fact that his side were also defeated last month by Chelsea after similarly being in the lead.
"It's difficult," he said. "It means we can compete with them.
"After Chelsea, I said that it is individual brilliance that makes the difference and to have a player as strong in character as Edin Dzeko to come on once again in the final minutes when his team needs him, and respond, that deserves great credit and continues to surprise me."
Villas-Boas must now lift his side for next weekend's eagerly awaited north London derby at Arsenal, although the Spurs manager insisted that would not be a problem despite his side having now lost three consecutive games to English opposition.
"The derby is a different situation," he said. "Most of the fans, the players, are already buzzing for the Arsenal fixture.
"It's a totally different game and that's positive for us because it represents so much for north London, Tottenham, Arsenal, that the players are able to get their minds right for it."
City, meanwhile, will host Aston Villa with England defender Joleon Lescott and Samir Nasri both expected to be available as they continue their comebacks from injury and illness, respectively.