Roberto Mancini's men are currently seven points behind the Premier League leaders, but have given themselves seven weeks to overturn the deficit.
And, having played a key part as City returned from eight points behind United to win the title last season, the Spaniard is confident of a repeat.
He told reporters: "It won't be easy, but our challenge is to be back level with Manchester United by the end of February.
"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.
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"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."
Sir Alex Ferguson's side stretched their lead at the top thanks to City's 1-0 defeat at Sunderland on Boxing Day, a result which Silva admits cause "anger" in the dressing room.
"The defeat at Sunderland was a hard blow for us to take. Nobody believed we would lose," he continued.
"As a team we have a huge desire to repeat our title success - nobody should have any doubt about that. But we know the Premier League is very open and if you give away chances, you can be beaten.
"Even so, there was a lot of anger in the dressing-room at Sunderland - and not only from the coach.
"Those three points were so important, because in our situation they could make the difference between winning and losing the title.
"If we don't win at places like Sunderland, it's nearly impossible to fight for success in this league. We have spoken about all this, about our irregular form. It's not a question of a lack of quality or bad luck.
"Rivals know how to play against us and each time they make it more difficult for us to win."