The North-West outfit have never lifted the coveted trophy, but their manager Pep Guardiola won it twice while in charge of Barcelona between 2008 and 2012.
In his first season at City, the Spaniard guided the team to the last-16 stage, but they were knocked out by Monaco across two legs.
On Wednesday, the Citizens will take on Dutch outfit Feyenoord in their opening group match on away soil.
"When you're at a club like City, you have to do your best to win all the trophies you compete for," Silva told the club's official website. "Of course, it's not easy to win a competition like the Champions League, but if you never try, you'll never win it.
"It's a special competition; first you have the group stages which is a tournament in itself, and then, when you pass through the group stage, it's a completely different competition again. To play a game at home and away, you have to play in a different way than when you're playing in the group.
"The thing I learned from last season is that you need a lot of confidence, you need to be at your best and, even when you're at your best, sometimes you lose, but because things are so complicated in the Champions League, you also need to have a bit of luck as well."
Silva joined Guardiola's team from Monaco in the summer window for a fee reported to be in the region of £43m.