The Spaniard was forced off in the first-half of the 0-0 draw at the Etihad Stadium and Manuel Pellegrini revealed after the game that he will not be fit for the return at the Bernabeu next Wednesday.
Speaking on BT Sport he said: "He has a problem in his hamstring. I don't think that he will be fit in one week."
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Silva was replaced by teenager Kelechi Iheanacho five minutes before half-time as City struggled to breakdown Real Madrid's rigid back line.
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Pellegrini claimed that the loss of Silva disrupted his team, but insisted that he is confident in making the final.
“I think we played a very intensive game, defended very well and we tried to create until Silva was injured," he said.
"After that we lost the ball too much. We couldn’t create clear chances but if you can’t win I think the best draw is 0-0.
“We thought they would play a slow game, that’s why we pressed very well, we worked as a team to have the ball. Unfortunately for us when we had the ball we couldn’t make the difference, we had two or three not clear chances, but we had options.”
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It was put to Pellegrini that City often do better away from home and he agreed with the assessment of his team, and explained why the first leg was a little more cautious than expected.
“Especially this season we’ve played very well away, we’ve beaten Sevilla, we beat [Dynamo Kiev], drew with Paris Saint-Germain so we go to Santiago Bernabeu with the same attitude, exactly the same to play away or at home,” he continued.
“We’ll have more space, Madrid must attack more. You never know what is good playing first at home. You can’t take too many risks because playing away is so important but now we’ll see in the second leg who will play the final.”
Additional reporting via Football Espana
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