The champions' surprise defeat at the Stadium of Light on Boxing Day has left City seven points behind bitter rivals Manchester United, and Silva, who suffered a frustrating afternoon in the North-East, knows that his side cannot afford many more slip ups in the second-half of the season.
"The defeat in Sunderland was a hard blow for us. Nobody believed we would lose." He told The Sun.
"There was a lot of anger in the dressing room - and not only from the coach.
"If we do not win at places like Sunderland, it is nearly impossible to fight for the success in this league."
Things have not gone to plan so far this season for City, with an early Champions League exit and the increasing gap at the top of the Premier League increasing the pressure on boss Roberto Mancini.
However, Silva knows his side must up their game sooner rather than later to get their supporters back on their side, and have any chance of retaining their Premier League crown.
"As a team we have a huge desire to repeat our title success, but we know that the Premier League is very open, and if you give away chances, you will be beaten," he added.
"It won't be easy but our challenge is to be back level with Manchester United by the end of February."