The Merseysiders sit just a point behind table-topping Chelsea with seven games remaining following a run of seven consecutive victories - form that has led to many fans beginning to believe that the club's 24-year wait for a 19th top-flight crown could be about to end.
Wednesday's 2-1 win over Sunderland at Anfield was preceded by supporters lining the streets to greet the arrival of the Liverpool team bus, and the division's in-form side go in search of an eighth straight win when they host Tottenham on Sunday.
However, while manager Rodgers accepts it is only natural for everyone associated with the club to feel excitement as the season draws to a close, he insists it is vital for players and supporters alike to keep cool under pressure - starting against Tim Sherwood's side this weekend.
"My message to the fans is to enjoy it," the Northern Irishman told the Liverpool Echo.
"We need the fans to stay calm. I know when you want something so much, that's easier said than done.
"They haven't been in this position for a while. I can understand that sometimes there is that bit of trepidation and fear, but what we're looking to put in place here isn't just for one season.
"We're looking to put something in place for the longer term in order to have sustainable success.
"The atmosphere at Anfield can be a real cauldron and now we really need our army of supporters to really get behind us.
"If a player makes a mistake, then encourage him. That's so important, because if they get that encouragement then they will get on the ball again.
"Amazing support at home is something we've had all season, Let's make sure in these last remaining games it continues along that way.
"Don't be frightened to really enjoy it because as players and staff, we will ... the players here are very relaxed and focused."
