Real are yet to concede a goal at home in the Champions League this season.
City did not manage a shot on target until stoppage time of the first leg, and their task against the 10-time European champions will be made harder by the absence of the Spaniard Silva, who limped off before half-time on Tuesday.
“David will not be fit next week,” said Pellegrini.
The Chilean is already set to be without Yaya Toure, who missed the first leg with a thigh problem, while another key attacking player, Samir Nasri, is not in their Champions League squad.
City, who play at Southampton in the Premier League at 16:30 BST on Sunday, also have less recovery time than Real, who play Real Sociedad at 15:00 BST on Saturday.
“Unfortunately for us we have one day less rest than Real,” added Pellegrini. “We tried to change our game and it was impossible so we need to play on Sunday.
“But we trust in what we are going to do in Spain – the players believe in what we are doing and I am sure we will give everything we can in that game.
“Of course Real have the advantage of playing the second leg at home.
“But, when we are away, we play very similar to the way we do at home and this season we have already had very good results playing away at Sevilla, Dynamo Kiev and Paris St-German.”
And Pellegrini insists that City have not missed their chance, despite failing to open up an advantage over a Real side that were without their superstar forward Cristiano Ronaldo in Manchester because of injury.
“They did not have Cristiano, we did not have Yaya. Karim Benzema played 45 minutes for them, the same as Silva who is very important for us.
“It was a very close game where we tried from the beginning to win. We pressed high and recovered the ball very well but we were not creative and we did not create a clear chance to score.”
City keeper Joe Hart, who made two crucial saves at the end of Tuesday’s game, is also confident that England’s last remaining representatives in the Champions League can continue their progress in Spain.
“Bring it on, we are ready,” said the England international. “We have a brilliant squad who are coming to fruition. It is a big game next week, simple as.”