Rafa Benitez's side are floundering in the Premier League title race after suffering their fifth defeat of the season away to Fulham on Saturday, a match which full-back Johnson missed through injury.
And their European ambitions are also hanging in the balance after back-to-back defeats at the hands of Fiorentina and Lyon ahead of Wednesday's crucial return fixture away to the French side.
England international Johnson knows the implications of the Merseyside giants failing to progress to the knockout stages and does not want to even consider the prospect of slipping into the Europa League.
"It would be a disaster for this club not qualifying for the knockout stages - but it's not something we are thinking about," he told the Daily Star Sunday.
No consolation"We have still got to believe we can do it. We don't even want to start thinking about the Europa League.
"It will be no consolation at all. It's not the aim and it's not the plan because we want to be in the Champions. It is one of the main reasons why players want to play for a big side.
"The Champions League is the best club competition there is. I played in it a few times with Chelsea and playing in it again was something that I was looking forward to doing.
"And I would love to go on and win it with Liverpool. But really I don't want to look too far ahead because we have made things very difficult for ourselves in the last two games.
"On paper we should be winning this group. The Champions League is just as important to us as the Premier League.
"They are both massive competitions and we like to do well in them both. The further that we get in the Champions League and the closer we get to the title, the happier the club will be.
"But playing in Europe, as we have shown over the last few years, suits our style."
FightFormer Chelsea and Portsmouth defender Johnson admits Benitez's men need to take maximum points from their remaining fixtures against Lyon, Fiorentina and Debrecen to be sure of progressing.
Lyon currently head Group E with a six-point cushion over the Reds with Fiorentina, who face point-less Hungarian side Debrecen in midweek, enjoying a three-point advantage.
Johnson added: "We are three points behind Fiorentina, so we may need to win all three remaining games. Lyon have got to play Fiorentina as well, so somebody will drop points.
"We would be happy with three wins but Lyon are a fantastic team who score a lot of goals at home.
"Any away game in the Champions League is hard. We must stick together and fight for each other. Hopefully we can keep a clean sheet and come back with three points."