The Easter Road side have now lost five of their last six matches, slipping from third to sixth in the cinch Premiership having played a game or two more than the teams immediately below them.
Goals from George Harmon in first-half injury time and Alex lacovetti 12 minutes from the end secured back-to-back wins for the visitors for the first time since March which lifted them out of the bottom two.
Hibs were booed off and boss Johnson admitted the reaction was deserved.
"I felt for the fans, I felt for myself, and I felt we didn't do enough," he told BBC Sportsound. "Any criticism from that performance is absolutely fair. I've never been one to shirk responsibility and it wasn't good enough. I'm as disappointed as them. We're all fighting for the same cause here. I don't think it was lack of effort from the players. We huffed and puffed, but severe lack of quality, lack of decision making and a very good away performance that done a job on us.
"We believe that the squad as whole - and we haven't always had the best quality that we've got out on the pitch - but we have got more quality than we've shown in our recent form. We have to get back to the drawing board. There will be criticism of course, and that's fair, but at the end of the day we all went to do well for Hibs and we all have to come out fighting against Kilmarnock."
Hibs enjoyed 65 per cent possession and had 21 shots on goal, with only four hitting the target, while Ross County had six attempts with three on target.
"We were nowhere near good enough in the final third," Johnson added. "We let them off the hook far too many tiems with poor crossing delivery, We work on the crossing in training, they deliver good balls, and for some reason we come into games and it's not quite happening. Not enough players are on their game, and obviously I haven't performed well either today and I take the brunt of that."
Johnson pledged to work hard to turn things around as he looked ahead to welcoming more players back from injury after the World Cup break.
"It's always a collective. We're desparete to do well for the supporters. We have let them down today, absolutely. In those losses there have been some decent performances as well, but still our fragility has come out in the goals that we've conceded. We've got to get through to this break and have that opoortunity to bring players back from injury where possible, and quality players. Until then we've got to be a bit more resolute than we've been. I promise you we will be working all hours of every day to try and find a solution to be successful. That's why it's so disappointing today because the staff have put in a hell of a shift over the last couple of weeks, and the players have, and for whatever reason - quality play from the opposition and poor play from us - we haven't been anywhere near good enough. So I can only apologise and promise that we'll battle to create that cuase and continue to fight."