With just three games left of the season, the Robins sit nine points off the play off zone and with mathematically be knocked out of contention should they fail to win against the Swans at the Liberty today.
It would take a monumental run of results for them (both by them and other clubs) to take them into the play offs but Johnson isn't giving up even if he thinks that some of his players and supporters already have
He told the Bristol Evening Post "One of the things that disappointed me on Monday was that I didn't think that both on and off the field we felt it (was possible).
"When you look at the how the results went, we were still in with a chance. On and off the field I didn't think there was the same mentality of me and Milly (Keith Millen) because we thought we still had a chance (of making the play-offs).
When asked whether he felt the Bristol City fans had given up too early, Johnson replied: "I thought they did. A lot of them went home quite early and we needed them to get behind the lads right at the death.
"All the way down that side (Dolman Stand) was empty with 15 or 20 minutes to go. They (the fans) have been fantastic for most of the season and we are very proud of most of them. Unfortunately, a lot of people misread the situation. I think player-wise and supporter-wise it was a quiet day. We don't have many of those and I love them (players and supporters) to death.
"Sometimes, though, for whatever reason – whether it was what is happening on the pitch or vice-versa – they were quiet and we need them to realise where we are and how important that extra bit of help is sometimes.
"It is a big game for me and I am trying to pass that on to everybody," Johnson added. "We will see how people react to it because I didn't feel like people thought it was a massive game on Monday.
"Let's see where we are after Saturday. If results go our way perhaps people will start looking at things differently. While there is still a small glimmer of hope you have to keep working hard and that is what I am going to be doing."
