After Chelsea boss Jose Mourinho kicked things off by describing his team as a little horse after beating favourites Manchester City, the Reds boss described his side as the "chihuahua that runs in between the horses' legs" after a midweek victory at Fulham left them four points behind the leaders.
Rodgers has always insisted Liverpool have too much to do - and too little to do it with - to be in the title race but the verbal sparring has gone up a notch after Arsenal manager Arsene Wenger said that attitude smacked of a "fear of failure".
Mourinho responded with a barbed comment that Wenger was a "specialist in failure" but Rodgers is keen not to get drawn into what could be an exhausting merry-go-round of quips and digs in the final three months of the season.
"It is getting stupid now isn't it?" he said.
"It is probably more for the media, who will make more of it than it actually is.
"As a modern-day manager there are so many elements you have to have to your profile at this level; it is more than just the coaching on the field, it is managing the welfare of the players, media, and the psychology of it all has always been the case.
"That is always about dealing with the human nature of people and getting the best out of them while managing expectations.
"That psychological side is as important as dealing with technical, tactical and physical elements of football.
"I can only speak for myself and it (mind games) has nothing to do with me.
"I focus on the players and let them do the talking on the field. It is the job of the manager to release the pressure on the players to go and perform.
"It may affect some players but I think the majority of players with a strong mentality it goes over their head."
Asked whether one of the requirements for a manager was to have a thick skin Rodgers replied: "It is imperative."
Rodgers maintains his fourth-placed side will struggle to mount a title challenge, even with just 12 matches remaining, but stressed that did not mean he was trying to ease the disappointment of not succeeding.
"Jose made the comment when I came in here (in the summer of 2012) that the conditions were such it would be a miracle for us to win the league and I don't think it's changed that much," he added.
"I don't think any manger working at this level would be proud to fail.
"It is one of the things which drives you on, in your personal ambition and ambition for the club.
"Jose is a wonderful manager and has had great success, Arsene Wenger has had success in a different way at Arsenal.
"If you are challenging at the top of the most competitive league in world football then you have to have something about you.
"It is going to be a really interesting last 12 games, it is set up brilliantly."
Despite what Rodgers' says publicly, Liverpool's chances of sustaining a title push rest with strikers Luis Suarez and Daniel Sturridge.
Suarez has 24 league goals and Sturridge 19, with the England international looking to set a club-record ninth consecutive scoring appearance against Arsenal in Sunday's FA Cup fifth round tie.
"He is up there with Luis as the best finisher in the league," said Rodgers.
"When Daniel is through on goal you are surprised when he misses.
"He is outstanding in the one-v-one and he has great variety in his finishing and both him and Luis are outstanding goalscorers.
"I think when he has consistently played he has scored goals.
"Goalscorers are like that - some will go through different spells and not score for six or seven spells and then they get seven in 10.
"I think Daniel has shown when he plays enough games he scores and scores regularly and Luis is the same."