Ambitions are high at Eastlands but recent results have seen Roberto Mancini's side slip five points behind Manchester United at the Premier League summit.
A win over their arch-rivals this weekend would cut the gap to two points but Silva would be happy enough with any top-four finish in his first season at the club.
"A good first season for me would be to qualify for the Champions League or to win a trophy," he said. "We will fight for the league title all the way and try to win the other competitions but the target is to finish in the top four.
"Within two or three years it will be normal for City to be playing in the Champions League every year, so I hope we can be on a par and challenge the best clubs around the world.
"I enjoyed six years at Valencia, they discovered me as a footballer and they will always be a special club for me. But the time was right to seek a new challenge and I am thrilled about how things have gone so far.
"The league here is one of the best in the world and I desperately want to bring success to City and win trophies.
"One thing is for certain, over the last few years City's image has grown massively in Spain. The project here is getting more important with every year. It's very exciting that I'm now part of it."
Silva has been an astute signing for City and star striker Carlos Tevez labelled the Spanish playmaker as one of the club's top acquisitions.
"David is the best signing we have made," said Tevez. "He is the type of player who can win you the game. He can provide you with the sort of pass that puts you through one-on-one with the goalkeeper.
"He has freshened up the team and brought a new dimension. We have the players here. The thing we need to do is build the team that the people and all of us want to see.
"It's always a big source of motivation to play alongside great players like David, Edin Dzeko and Mario Balotelli. We have a forward line that can do a lot of damage to opposing teams."
