Nahki Wells had put the Terriers ahead before Tom Lawrence grabbed an equaliser, but Adam Clayton lashed in a late winner for the visitors to leave the Glovers six points from safety and rooted to the bottom of the table with two matches remaining.
The Glovers must win both of their remaining games and achieve a 13-goal swing over Birmingham, while also hoping Lee Clark's side lose their next three matches.
Johnson said: "We knew we were in a division that we had to enjoy and we have done that. Our supporters have enjoyed the Championship and we're definitely competing above our status.
"Hopefully being back in League One we can regroup and challenge to get back into this league.
"We need to become bigger as a club, have better infrastructure, better stadium and a bigger budget if we're going to be anywhere near keeping a team in the Championship. Our attendance today was around 5,000 - if you're in the Championship you can't survive on that.
"We've been great and the fans that have turned up have enjoyed the effort shown, and we have needed a lot of effort to get to our total.
"Although we're down we're looking at it philosophically, and if we come back up we need to be ready to be bigger.
"We owe it to the other teams in this division to keep giving our best and make sure we try to pick up points in our last two games."
The last-gasp victory secured the Terriers' Championship status for another season, much to the delight of manager Mark Robins.
He said: "That was tough to watch and this Championship can do all sorts to you. We've got competent players but they looked less than competent in the first half and kept giving the ball away.
"The Easter period is always tough with the quick turnaround in games. The same players are used and it becomes a real slog. I'm just grateful we could see it out and Adam's winner was outstanding.
"There's a big relief out there because we needed the three points desperately today. I'm still disappointed we're talking like that and this season has to be a lesson. It's not going to the very last game this season so that's progress, but I'd like a long summer of hard work to try and improve us for next season.
"My thoughts can now turn to the summer because we've secured our status.
"It's not a case of 'job done and down tools', it's a case of getting some rest because we'll need it ahead of the two games coming up."