Bookmakers slashed the odds for the Northern Irishman being the next Premier League manager to lose his job following a 2-2 UEFA Champions League draw against Ludogorets in midweek.
Liverpool had lost four games in a row prior to that result in Sofia and they sit down in 12th place in the Premier League after only just missing out on the title last season.
Rodgers, though, is turning a blind eye to speculation over his future ahead of Saturday's clash with Stoke City at Anfield.
He said at a press conference on Friday: "A few months ago I was manager of the year, now I'm tipped to get sacked. All I can focus on is what you can control.
"This is a different challenge. Everything hunky dory for 18 months, It's a different set of cards I've been dealt now."
Rodgers added: "I read very little of what is said or not. Everyone nowadays has an opinion whether a player, supporter... people are paid to be critical, some aren't.
"You don't forget the support in moments that are difficult on and off the pitch. I'm thankful we have guys here like Ian Rush, Robbie Fowler, Kenny Dalglish - legends of the club - who are unequivocal in their support.
"The focus will always be on the players and be the best they can, to win football games. When we were going for the title, we still had criticism by players, pundits - but we nearly did it in the end.
"I'll always respect opinions of former players of this club, I'll take on board any sort of criticism but I'm more focused on my own job."
Goalkeeper Simon Mignolet came in for criticism following his error for Ludogorets' opening goal, having already come under fire as a result of some unconvincing performances for the Merseyside club.
Former Liverpool keeper Bruce Grobbelaar was particularly scathing with his assessment of the Belgian, but Rodgers revealed that the former Sunderland man has taken the flak on the chin.
He said: "He's coping well. It's never easy. However it comes, criticism whether deserved or not, you don't like it. It's part of the sport and part of the game.
"We're losing games of football, not playing so well, it's what happens and when you're at a club like Liverpool the focus on you is magnified and you have to accept it as part of the job."
The Liverpool boss revealed that striker Mario Balotelli will remain sidelined for the game against Mark Hughes' side due to a hamstring injury.
