And he now setting his sights on second-placed Manchester City.
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 now 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."
Premier League Top 4 Finish 12/13 Top 4 Finish: Liverpool 150/1
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