City won 2-0 at Arsenal on Sunday afternoon to close back to within seven points of local rivals Manchester United, who had won 2-1 at home to Liverpool earlier in the day.
Goals from Edin Dzeko and James Milner were enough for City to beat Arsenal, who had Laurent Koscielny sent off after just 10 minutes.
City captain Vincent Kompany also saw red late on but the champions saw the game out and Silva believes one slip-up could prove vital in the run-in.
Asked if there was a sense that City could not afford to lose again, he said: "Yes, because if we lose, then suddenly the gap is 10 points and that is when it gets really difficult.
"But if we keep fighting we hope that they will falter."
United have been in control of the title race since Robin van Persie's injury-time winner at the Etihad Stadium on December 9, but Spain international Silva vows that City will keep putting pressure on the 19-time league champions.
He added: "All we can do, whatever the gap is, is keep going, every game, and put them under the pressure of knowing that if they lose a game or drop any points, we will get closer to them.
"That works the other way, of course, too, because if we lose we will get further away, but we cannot think about that. We just have to continue as we are. The league is still there to be won."
City bombed out of the Champions League at the group stages for the second year in succession but Silva is hoping United's progression in Europe could lead to them falter domestically.
"That could be an advantage for us," he said. "They have an important game against Real Madrid and we only have the league to think about. That could work in our favour."
City have won all but one of their league fixtures following their derby defeat to United.
They lost 1-0 at Sunderland for the second season running, but wins over Reading, Norwich, Stoke and Arsenal have kept them within touching distance of the league leaders.
Silva does not feel that it is a step up in performances, but rather a change in fortune which has led to a decent run.
"I think in the last few games it's not that we've improved particularly," he said. "Its just that we've had that touch of fortune which maybe we weren't getting earlier on, like in the United game, when they scored a lucky goal in the last minute.
"We are playing well and doing the right things, and then we are getting those moments of good fortune going our way now."
City confirmed on Monday that they will be appealing against Kompany's red card, shown by referee Mike Dean for a foul on Arsenal midfielder Jack Wilshere.
First-team coach David Platt told CityTV: "We feel as though there is a case.
"It is a difficult one for the referee because when you look at it live it certainly looks like what the referee would term as serious foul play.
"I think when you slow the incident down you see that Vinny takes the ball and it is only one-footed. I think opinion will be divided.
"He certainly goes to ground but he actually takes the ball. I wouldn't blame the referee for his decision but there is doubt as to whether it is a red card."
If the appeal is unsuccessful and a three-match ban upheld, Kompany would miss Premier League matches with Fulham and QPR and an FA Cup fourth-round tie against either Crystal Palace or Stoke.
There is also the possibility that an extra game could be added to the ban if the appeal is deemed frivolous, which would mean Kompany sitting out the visit of Liverpool on February 3.
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