After the club's worst start to a campaign for more than a century, the Reds now sit just four points behind fourth-placed Everton, with their record over the last 11 matches bettered only by the top two of Manchester United and City.
But having seen his players criticised early in his Anfield reign Rodgers now believes they should not be restricting themselves to thinking purely about securing Champions League qualification.
"They have been hammered left, right and centre by numbers of people," said the Northern Irishman.
"When you are a club that is the size of Liverpool then that criticism comes.
"It is well documented, which is incredible really, but when you have won the titles and championships you have before that will come your way.
"But I was quite calm because their focus and concentration has been first class, our mentality was very much relaxed as we can only worry about ourselves.
"The cause we created here was to continue to fight.
"We know what will come our way when you don't win games and we are trying to still improve so the feeling was fine.
"You can see in their performances it hasn't affected them and, if anything, we have grown from that and it has been the lever for us to continue to work well.
"Everyone has their opinion on Liverpool and I understand that because of the standards set by this club in the 1970s and 1980s.
"But for a club that has been very poor and disastrous by all accounts from other people we lie four points off top four.
"For me the ambition is to grow higher. We are 11 points off second and that can all turn around very quickly so you need to get consistency -- and that is what we have at the minute."
Many of the players criticised -- Stewart Downing, Jordan Henderson, Jose Enrique and, in particular, Joe Cole -- were signed by Rodgers' predecessors Kenny Dalglish and Roy Hodgson.
Liverpool's former director of football Damien Comolli, who helped bring most of those players to the club, has said they have all been judged too early.
"I don't know what Damien said and it's none of my business," added the Reds boss, who was pleased to see Cole score in Sunday's 3-2 win at West Ham.
"It was important for Joe to contribute. This season has been very difficult for him because he has been injured for the majority of it.
"The responsibility has always been with the players and if Joe continues to work how he has
been when he gets the opportunity he has to take it.
"He works very hard at his game and when the chances come I know in his own mind he wants to take them and be effective for the team.
"That is the challenge for all the players. It is a challenge for us all to improve and we want to keep rising up the table."
Top scorer Luis Suarez returns after a one-match suspension for the visit of Aston Villa tomorrow and although his goalscoring exploits have been impressive, the Uruguay international still has to carry the stigma of being labelled a diver.
However, Rodgers believes recent incidents involving other players have highlighted that there is a wider issue to be addressed.
"Luis Suarez was held up as the only one that seemed to be doing it," he said.
"Whenever many other players were doing it, both British and European, it seemed to go very quiet.
"It's something that is the responsibility of the players. The managers can only guide and give their opinion to the players.
"You see it now becoming a part of the game but it's certainly something we want to eradicate.
"It's difficult for the referees because they are having to make that judgement straight away.
"Pundits and others get a chance to review it a number of times."
Rodgers also said the club had learned their lesson from last summer's transfer window when their pursuit of Clint Dempsey prompted a complaint from Fulham, which was only withdrawn following an apology from Reds chairman Tom Werner.
"There is nothing for me from a managerial perspective to add to it," said the manager. "As a club we've all moved on from the summer and when January comes whatever experiences we had then we'll be better for."