The Liverpool manager saw goals from Luis Suarez, Raheem Sterling and Steven Gerrard see off Southampton 3-0 at St Mary's Stadium on a day when Arsenal slipped to a 1-0 defeat at Stoke City.
With Liverpool now four points off leaders Chelsea and level with Arsenal, Rodgers remains calm when it comes to talk of a title challenge.
"Everyone speaks about Chelsea, Arsenal and Manchester City and rightly so. For us, we're just concentrating on ourselves," he told Sky Sports.
"We just want to keep improving, mentally we're getting stronger all the time. With 10 games to go, we'll just see where it takes us.
"I just want to enjoy watching the team. We only want to win the next game, there's no point getting ahead of ourselves."
Suarez - making his 100th Premier League appearance - had a hand in all three goals as he scored the first, assisted the second and was fouled by Jose Fonte for Gerrard's penalty.
However, Rodgers reserved special praise for Sterling after he came off the bench to score on his 50th Premier League appearance.
"This is a difficult place to come, it was an all-round outstanding team performance with and without the ball," he continued.
"Raheem is a young player, he's been brilliant. I just thought as the game went on he was someone we could bring on with his pace and trickery.
"People see him as a wide player, but we don't want to pigeonhole him. His touch is good, he can connect the game well and (he produced) a good finish."
