Talks to extend his current deal, which expires in the summer, ground to a halt in the close season when the two parties reached an impasse over terms.
It is understood the Reds wanted Johnson, who turned 30 in August, to sign a reduced-terms contract to reflect his age but he is unwilling to accept that.
"I have enjoyed the majority of the six years; I've had some good times and some bad times, but if I haven't got a contract then I can't stay," said the England defender.
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"Of course it plays on your mind but that is when you have to be professional and try to do a job for your team, and I respect my team-mates and I want to put in a performance for them.
"I want to play for a club that wants me - I am not going to go crawling to anybody. The club know where I am and they know the situation.
"There were minor talks at the end of last season but nothing I could accept or reject."
Asked whether he was surprised Liverpool had not made more effort to extend his contract, Johnson added: "I have not really thought of it like that.
"Whether it is football or business I don't really worry about things I can't control.
"All I can do is try to keep doing my job every weekend and whatever will unfold will unfold."
As he enters the last six months of his contract the right-back is entitled to sign a pre-contract agreement with overseas clubs, but is remaining focused on his immediate future.
"It is not my business to talk to other clubs at the moment," he said.
"I want to play my football, keep winning for Liverpool and I want to respect my contract, and that is what I am willing to do."
Johnson's first goal since December 2012, stooping to convert a low header after Rickie Lambert's header had come back off the crossbar, gave his side a 1-0 victory over Stoke.
Having ended a three-match losing run in the league the defender believes a top-four finish is still very much within their grasp.
"You enjoy winning games, scoring goals and being involved in assists - they are the great parts of football so on a personal level I am very happy," he added.
"Nothing has changed from last year. The backroom staff, the playing staff are fighting for the same cause and the objective is still the same, but in football you go through some sticky patches.
"The quality is not in doubt, it is about confidence and trying to put a run of performances together."
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