Just four points separate leaders Chelsea and the in-form Reds, who usurped Manchester City and Arsenal in the Barclays Premier League standings with their 3-0 victory at Southampton.
Luis Suarez opened the scoring early in the first half at St Mary's and, having withstood the hosts' impressive response, Liverpool went out of sight thanks to goals from Raheem Sterling and Steven Gerrard.
The result extends the Merseysiders' winning streak to four matches in the league, while they remain unbeaten in this calendar year - yet manager Rodgers remains keen to avoid talk of the title.
"I'm not focusing on that, to be honest," the Reds boss said. "I'm focusing on winning the next game.
"I think we've had an outstanding performance today, a really significant performance against a very, very good side with an excellent manager.
"The players were tactically brilliant today and we scored three and maybe could have had another five or six goals.
"But we'll just stay calm. There are 10 games to go now, we're in a good position and we just want to continue working at the level we are at."
Asked if he had deliberately banned title talk, Rodgers said: "No, we stay calm. It is great for the supporters to dream.
"What is great for them is that they have seen the evolution of this team over the last 18 months and we've consistently being progressing and performing at a really good level.
"So we stay calm, we don't get too carried away. We just always focus on the next game.
"After Swansea we always knew this would be a really difficult game today. They have scored in all-but two games here, have some real good players and have an excellent manager.
"So for us to come and play like we did today and find a solution to nullify that threat was impressive by the team."
Rodgers may not want to talk about winning the league, but with Suarez leading the line it is hard to see their momentum slowing.
The Uruguay international ended a five-match goal drought by opening the scoring at St Mary's and marked his 100th league appearance for the club with a key role in the other goals.
"Well, it helps when you have a team and a squad," Rodgers said, when asked about Suarez's influence.
"Luis has been sensational but I think everyone last week was saying he scored four goals in the last 33 goals that we have scored, but he's a huge influence in the team.
"But today was very much about the squad and the collective.
"Everybody had to do their job, the goalkeeper made a great save and we looked a real threat going forwards."
Suarez certainly played a key role for Liverpool at St Mary's, with Southampton manager Mauricio Pochettino saying he is "definitely one of the best in the world" right now.
The Argentinian also believes the Reds can mount a "very good challenge" for the title after the win, which he feels could have easily gone the other way.
"We created many chances in the first half and we deserved a lot more from that first half and it should have been a different result," Pochettino said.
"But we needed to be more clinical in the first half to get a different result going into the end of the half.
"We were unlucky not to score and then Sterling came on and with his first touch it was 2-0, and it was very difficult from then on to kick on and keep pushing.
"I thought overall with the team's performance it was an unfair result, but I do have to say Liverpool were a lot more clinical than we were."