"I spoke to the owners and they wished me good luck and sympathised with the frustration I must have been feeling after Wednesday night (the defeat to Wolves)," he said.
Asked whether he felt he had the owners' support Hodgson added: "I guess so.
"It is not about me. I am very pleased and honoured to have this job.
"It is about Liverpool Football Club and performances so I don't take the speculation seriously of course.
"I shall probably have to learn to accept I shall get a lot of brickbats.
"I take enough negativity from you guys (the media), today I am going to be quite blunt and I am not interested in anything negative.
"Had we won on Wednesday night you would now be asking me about the Champions League but because we didn't win on Wednesday I am asked about the negativity which, to be honest, is being created here in this room.
"That is something I have to live with but it doesn't affect me in my job because my job is to make certain the performance of the team today was the performance you saw.
"I am going to be satisfied the team has given the performance I want, they want and the fans want and a happy evening is ahead."