Chelsea’s defeat to West Ham earlier in the day had presented an opportunity for City and Liverpool to leapfrog the Londoners – an opportunity both sides took advantage of.
However, Sterling asserts City are not concerning themselves with other teams’ fortunes and instead are concentrating on doing whatever it takes to win the next game.
“We know what our job is and we can’t really be watching what the others are doing,” he said.
“We just need to keep working away and getting three points each time and that is what we did [on Saturday].
“[Vicarage Road] is a very difficult ground to come to and we knew it was going to be tough.
“It is one of those games where you have got to be up for it because they can punish you.
“[Watford] make it really difficult with second balls and you have got to be up for every battle. I thought we did that brilliantly.
“To be away from home for two fixtures on the bounce, you need to keep that mentality.
“Games come thick and fast. All you can do is just keep focusing on the next one and getting three points each game. That is all you can really focus on.”
Sterling also hailed the influential display of Bernardo Silva, who bagged a brace against the Hornets to continue his excellent scoring form, in which the Portuguese playmaker has bagged five goals in six games.
“He has been in incredible form and long may it continue.
“If you look around in our team there are a few players in each position. Every player starts for their national team.
“The manager has got loads of players at his disposal and it is a great thing to have in a team.”
Reflecting on his own dazzling displays, Bernardo expressed his delight, crediting City's incredible strength in depth as a key component in his and our recent success.
“I'm happy with my current moment,” he declared. “I'm happy with the moment of the team.
“The way this team is built, even when a player is out, we don't miss the player and the team works well.
“It's a real team – not just one player or two. We are eleven players on the pitch; a few more on the bench.
“Every one of us gives our best and it doesn't matter who plays, everybody performs and plays to win.
“Things went well [on Saturday]. We are training well.
“We have a lot of games at the moment and we need to continue the same way.
“We are just at the beginning. It's going to be a long and tough season. We know how good our opponents are but we just want to win.”