The Scottish Football Association on Wednesday offered the Dundee manager a one-match ban after he labelled Alan Muir's decision to award Aberdeen winger Peter Pawlett a spot-kick as "diabolical".
Dundee have confirmed they would challenge the punishment but Brown now admits he was rash to say in a radio interview on Monday that he would resign if hit with SFA action.
He told Press Association Sport: "We're appealing the charge and hoping it will be overturned. But as for the other stuff, well we all say stuff in the heat of the moment.
"I made a comment earlier in the week (about resigning) but I've spoken to our chief executive Scot Gardiner and we've had a good long conversation. I've got a two-year contract at Dundee and I will be honouring that."
Gardiner, however, insists Brown was told in no uncertain terms that his offer to resign would not be accepted after he was charged with "making comments in a media interview that criticise a decision and the performance of the match officials in such a way as to indicate incompetence".
He said: "I'm not sure if it was heat of the moment. I just think John was being honest. When I told him about the charge yesterday, he re-iterated his position. I made it very clear to him that we would not accept his resignation. A lot of people love John and a lot don't. The one thing you can say about him is that he is straightforward and honest. He's a man of his word and if he says something, he'll stick to it.
"We've shown a lot of faith in John and so have the players. That's why we've got the results we've had. The fans have got behind him too, so I made it very clear that I was not accepting his resignation.
"He accepted that in the end over a number of phone calls. He's back at work 100 per cent focused. I wasn't pleading with him, I was telling him he wasn't going anywhere. He's got a two-year contract. We believed in him when we brought him in, he exceeded those expectations and because of that he was rewarded with his deal.
"We believe he is the man who is going to lead us back into the SPL. I understand why he said what he said but he's got a job to do."
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