Rodgers has also come under fire from former skipper Steven Gerrard, who suggested in his autobiography that the Liverpool boss was guilty of over-confidence when the Reds were challenging for the title in the 2013-14 season.
After a stuttering start to this season, Liverpool are 13th in the Premier League but only four points off fourth place, which remains the minimum target for Rodgers.
Rodgers faces a fight for his Anfield future after an underwhelming Capital One Cup victory over Carlisle United, which saw the League Two side force the Reds into a penalty shoot-out.
Former Real Madrid manager Carlo Ancelotti and ex-Dortmund manager Jurgen Klopp has been strongly linked to taking up the job at Anfield.
When it takes you penalty kicks to beat Carlisle United, the team with the worst defense in League Two, maybe it is time to take your football club in a new direction. If you’re not winning, that will intensify. I walked in here as a 38 year old manager and as I sit here I am much better manager, but I understand I must get results.
“I am never complacent enough to think (my job is not under threat)”.
“You always want a fully-fit squad to pick from, but it’s the nature of it”, Rodgers added. “I don’t shy away from the fact that you need ot get results and on top of that you need to be performing well in order to stay in work”. “But it doesn’t frighten me”, he said.
“I hope to be a manager for another 20-odd years – and I accept that 20 years probably won’t be at Liverpool“.
“I think [Rodgers] went on too much, since he got the job, about his philosophy”.
Speaking ahead of Saturday’s crucial home game against Aston Villa, Rodgers acknowledged the speculation regarding Klopp and Ancelotti and said he would “totally respect” the decision should Liverpool’s owners decide to sack him.
Rodgers offered a reminder about what he achieved in leading Liverpool back into the Champions League and to the brink of the title when he had “world class players” at his disposal in 2013-14.
“They are not dissecting the game like I do every week”.
The manager is struggling with a lengthening injury list, as captain Jordan Henderson will be out until November after breaking a bone in his foot.
Forward Roberto Firmino has a suspected cracked bone in his back while Dejan Lovren is also sidelined for a few weeks with a ligament injury.