Liverpool are now second, a point behind leaders Chelsea, with City two points further back with two games in hand.
“It’s up to other teams to lose, so we will keep working hard,” Rodgers said.
“I’m not playing it down, I don’t play silly mind games. If City win their games, they win. It’s simple maths.”
Rodgers’s approach mirrors Chelsea boss, and former mentor, Jose Mourinho, who has said Manuel Pellegrini’s side remain on course to repeat their championship success in 2012.
But the Northern Irishman admitted he would be “lying” if he said his team were not in the race for their first top-flight title since 1990 after recording their seventh consecutive league win.
Liverpool host City on 13 April and Chelsea on 27 April during their season run-in.
Rodgers added: “I’m concentrating on my team and Jose Mourinho is saying what I’m saying.
“Manchester City have games in hand and the squad to win the title and the Champions League, Chelsea likewise, but we are enjoying being up there.
“We are second, I’m not going to say we are not in it because I’d be lying.”
Steven Gerrard’s free-kick and Daniel Sturridge’s 20th league goal of the season put Liverpool on their way to victory at Anfield, but Ki Sung-Yueng’s header and a late miss by John O’Shea ensured there was relief at full-time after an anxious finish.
Sturridge’s goal meant he and Luis Suarez are the first Liverpool strike partnership in 50 years to score 20 league goals each, emulating former Reds forwards Ian St John and Roger Hunt.
But Rodgers chose to praise the collective effort of his players, saying: “It is a great achievement for the team. Suarez and Sturridge are soloists, individuals that fit into the collective picture. They are top-class talents.”
Written by Steve Milne
