The Northern Irishman, who is under fire after Wednesday's League Cup humiliation at home to his former club Swansea, has warned fans there is no prospect of a quick fix at Anfield.
But he is desperate to be given the chance to finish the job he has started.
"I have signed a three-year deal here and the process will go on beyond that. Hopefully I can be here to keep building it. I am loving every minute here. I came for the challenge, but it is easier said than done," the Daily Mirror quoted Rodgers, as saying.
"I just look at the stats over the last three years and it has been going the other way. Our job was to spin that around and, through a lot of hard work, get us on an upward spiral," he added.
Rodgers also questioned the lavish spending on flops before he arrived but stopped short of criticising former boss Kenny Dalglish, who green-lighted the vast amounts paid for Andy Carroll, Stewart Downing and Jordan Henderson.
"The investment in a small period of time was big for the club. I was also brought in for a reason. It was going to take time," he said.
"The owners are fully aware of that as well. The support from them has been fantastic - they have the helicopter view of the big picture," he added. (ANI )