But Harry Maguire cancelled out Sadio Mane's opener to ensure a loss of two points for the Reds and West Ham's Michail Antonio did likewise against Jurgen Klopp's team on Monday.
In between those games, Pep Guardiola's men saw off Arsenal 3-1 thanks to a Sergio Aguero hat-trick and goals in stoppage time at the end of each half from Aymeric Laporte and Gabriel Jesus sealed a 2-0 win at Everton on Wednesday – moving them above Liverpool on goal difference for the first time since December, albeit having played a game more.
"After Newcastle, it was very tough on us," Portugal playmaker Silva told reporters.
"We were very disappointed, more than anyone else. The players, the staff, we were all very sad, because we all thought we had lost the league in that game.
"Fortunately, Liverpool drew against Leicester and that gave us a little bit of hope. Then there was another draw against West Ham and that meant the race was on.
"Mentally, this is a big boost for us. We will try to keep doing our job and not relax as we did against Newcastle."
City face another stern test on Sunday when they host Chelsea, having suffered their first Premier League defeat of the campaign against Maurizio Sarri's side last time they ceded top spot to Liverpool.
Silva, who was identified as a standout performer of late by Guardiola, has no doubt his team-mates are equipped to battle for honours on four fronts.
"In my opinion, it is not problematic at all - especially when you have a squad like ours," he added.
"If we don't have injuries then I think we can cope, no problem at all. It is good to have lots of games as it means we are fighting for everything. Mentally it is good. We will try to do it."