The Gunners extended their stay in the FA Cup with a 3-2 win over Aston Villa on Sunday while City bowed out to Manchester United in the third round.
City exited the Carling Cup at the semi-final stage to Liverpool on Wednesday and they are now facing Europa League football after missing out on qualifying for the knock-out stage of the Champions League.
However, City are top of the Premier League table ahead of the Red Devils while Roberto Mancini's troops are 18 points ahead of Arsenal and current favourites for a first-ever Premier League crown.
City have spent hundreds of millions of pounds assembling one of the best squads in European football, although Gazidis insists Arsene Wenger's side incorporate a 'value system' that promotes long-term sustainability.
"We're in three competitions this year. Manchester City would love to be in three competitions," explained Gazidis. "They're not. So money is not everything in this game.
"I don't disagree that it's important. But we do things based on a value system. We're about creating star players, not about buying them.
"We're about what happens in a team, between players, not individual superstars. And that's an inspiration to people around the world. We can't afford to compete with oil money and we can't afford to compete with super-wealthy individuals from Russia.
"But the more important thing about our model is that it's sustainable. Our business model means we can continue to do what we're doing forever.
"We're proud of the way we do things and we're proud of the results that we're able to produce from that."