The Blues claimed commanding 2-0 away win in their quarter-final tie with Porto on Wednesday.
Speaking to the club's website, Silva said: "We're going in the right direction right now, getting wins and feeling really motivated but we are also in a new beginning, with a new coach and a new style.
"Of course there are ups and downs in a long season, especially when the team is very young, but I believe we're fully capable of getting far in the Champions League.
"We've got great quality and, especially in knockout games, you just have to hope the opponent isn't having a good day and that you are. This can change the season completely for a team with big dreams."