Things came to a head on Wednesday when Liverpool lost 1-0 at home to Wolverhampton Wanderers, their eighth league loss of the season and one which left the 18-times league champions just three points above the relegation zone.
The crowd chanted "Hodgson for England" and even held up banners saying "Come Back Rafa" leading to under-fire Hodgson to say after "the famous Anfield support has not really been there ever since I came here".
He also said he hoped the fans "became supporters" which sparked angry comments on internet sites and prompted an online petition to have Hodgson sacked.
The Englishman is the favourite with bookmakers to become the next Premier League manager to lose his job.
Speaking on Friday, Hodgson attempted to placate the fans before Saturday's crucial home game against Bolton Wanderers.
"I certainly regret it if I offended the fans in any way, it was no way meant to cause offence, it was a purely defensive comment," Hodgson told a televised news conference.
"I was taking responsibility and quite prepared to accept it on the chin that I would be the one in the firing line for the team's poor performance.
"I understand and empathise with them and I'm disappointed if that's been changed into me attacking the fans there is no way I would want to do that and there is no way that would be justified because they are the best in the country.
"When I say support, i think they support the club and the man who has been given the job as manager of the club but it's been an uphill struggle for me from the start and I don't necessarily think they got behind the appointment and there's no reason why they should.
"I believe they are very much Liverpool fans and very much behind the club and if we start to turn things around and get the results then they'll be behind us all."
