Pep Guardiola's City eliminated Real in the last 16 while defending champions Liverpool were knocked out by Atletico Madrid.
City are firm favourites heading into Saturday's quarter-final against Olympique Lyonnais but Silva said they would not get complacent.
"Anything can happen, Juventus were knocked out by Lyon, we lost against Tottenham Hotspur last year in the quarter-finals," Silva told the City website.
"We have seen lots of surprises. It's very difficult to predict the results in this competition."
"The fact that Liverpool are out, Real Madrid are out: it's not going to make our path easier ... All the teams in Lisbon are here because they deserve it. We need to be at our best level to win the games and try to reach the final."
Silva, who was born in Lisbon and began his career at Benfica, said the prospect of lifting the trophy on home soil gave him extra motivation.
"Winning this competition has always been a target for the players and the club. It will be very special to win it. For me, even more so because it's my city," he added. (Reporting by Arvind Sriram in Bengaluru; Editing by Peter Rutherford )