The Reds qualified for the Europa League with a sixth-place finish last season but ended the campaign in disappointing fashion with a humiliating 6-1 defeat by Stoke City.
Liverpool have the chance to make amends for that final-day thrashing when they return to the Britannia Stadium on Saturday for their Premier League opener and Rodgers says that he wants to repay the faith shown in him.
"I never take for granted the support I have had here," the Northern Irishman told reporters. "I also understand the disappointment of last year. I'm sure, after a game like Stoke, there was huge disappointment.
"Of course I have always been the one to take responsibility and rightly so. The anger goes towards the manager and I accept that.
"Yes, I need to regain their trust again. It has been an incredible journey since I came in here and it is an absolute privilege to manage this club and have the supporters behind us but, of course, you have to do well to earn that support and I know I need to earn that again."
Rodgers's job security came under threat at the end of last season following a string of poor results which saw Liverpool collect just eight points from a possible 27 but the 42-year-old remains confident in his ability.
"You never take your position for granted. You certainly can never be complacent," he added. "The owners have given me great trust since I have been in here and, in the main, I have had a great response from the players.
"I have confidence in how I work. It certainly didn't take away from my beliefs in my work but it sharpened that I needed to refocus and look at how we could take the club forward.
"I'm as driven now – if not more – as the first day I came in here. We want to put a disappointing season behind us."
