Philippe Coutinho secured a vital 3-2 victory over Manchester City on an emotional afternoon at Anfield to move the Reds seven points clear of Manuel Pellegrini's men, who still hold two games in hand.
Raheem Sterling and Martin Skrtel put Liverpool in control in the first half, only for City to roar back after the break with goals from David Silva and a Glen Johnson own goal.
Liverpool's destiny remains firmly in their own hands after an astonishing run of 10 successive wins, and further victories over Norwich, Chelsea, Crystal Palace and Newcastle will see them crowned champions for the first time since 1990.
Rodgers told Sky Sports: "The expectancy of this football club is a challenge every day. Our objective is to stay where we are, there is no question about that.
"We've been put under pressure in every game that we've played. But you see the level and the quality of our football - it was fantastic today - so we're clearly coping with it.
"It was a remarkable performance. I thought we were incredible today. I think the world watching that would see a team with so much spirit and so much quality.
"It showed you the character in this group to come back, to get our composure again and to score a brilliant goal.
"We were well on top in the first half, 2-0 up and could have been more. But they have got top players, and top players respond and show character and they got themselves back into the game.
"I said before the game that it was a significant game and it may end up being a significant one, but we've got Norwich next week.
"It's about enjoying this because Man City are a wonderful team. We'll recover well and we're not going to vary from what we've always done, which is to concentrate on the next opponent."
The match was preceded by an impeccably observed minute's silence in memory of the 96 men, women and children who died in the Hillsborough disaster, with the 25th anniversary of the tragedy falling on Tuesday.
Captain Steven Gerrard, whose 10-year-old cousin Jon-Paul Gilhooley was one of the victims, had tears in his eyes at the final whistle, and Rodgers admitted that the memory of their lost fans proved an inspiration.
The Reds boss added: "It was a wonderful atmosphere. I'm sure it sounded loud on TV, but down on pitch-side it was incredible.
"There is always an emotive side around this time, people were wondering if that would affect us. But we live with that every day.
"The families and the victims of Hillsborough are with us every day, in our thoughts. It was an inspiration for us, rather than something that would hold us back."