The Easter Road side were beaten 3-1 in Glasgow despite a spirited away performance from the ten-men, who had Elie Youan harshly sent off in the first half by referee Steven McLean.
There was also a feeling the penalty which enabled Celtic to equalise through Jota was another error by the official.
CEO Ben Kensell made his feelings known to Scottish FA officials after the game in what was described as a “heated exchange” as they demanded answers regarding the official’s performance.
Johnson says the club’s response came from a source of “passion” but he insists he wants to be on the same side as the authorities to help improve the level of officiating in this country.
"It was Ben Kensell who ended up having more contact in terms of written and verbal communication with the SFA and the head of refereeing and I think it was just a case of me controlling what I could control and concentrating on the players,” he said prior to this weekend’s match with Motherwell.
"I think the starting point is that you feel injustice, and that makes you angry and upset because we're all passionate about doing well.
"But we want to help. No one's trying to go to war with anyone – we want to help the Scottish game be as good as it can be and if we can add any influence or guidance or advice that helps then great and if not, then we just crack on.”