The reigning champions trail United by seven points ahead of a big weekend in the title race with City travelling to Arsenal and United playing host to Liverpool.
City clawed back an eight-point deficit on United last season to claim the title and Spanish playmaker Silva believes they can do it again.
"It won't be easy, but our challenge is to be back level with Manchester United by the end of February," said Silva.
"Last year we saw how they were in front by quite a lot of points, and we won the league anyway, so it can be done.
"Our goal this season was the Champions League. But now that chance has gone, we want to win the Premier League and dedicate the achievement to our fans.
"The only way to do it is to work harder every day and to avoid more stumbles. Perhaps being knocked out of Europe had an influence.
"But now we need to react and to demonstrate that City are the English champions and intend to remain so. There is a long way to go, but we can't allow United any more advantage at the top of the table.
"The future is in our own hands but we have already shown how powerful we can be during our worst moments in the past year."
Arsenal v Manchester City is live on Sky Sports 1 this Sunday. For more details click here
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