Brown announced his decision after the Latvia game
He announced his decision after the 2-1 win over Latvia - a result which proved irrelevant as Croatia beat Belgium to ensure Scotland finished in third place in Group Six.
Brown said he had decided that this would be his final campaign some time ago.
The decision brings to an end Brown's eight-year term as Scotland manager.
In an emotional post-match media conference, Brown underlined that he wanted to remain as technical director with the Scottish Football Association.
"I wanted the players to be the first to know," he said. "It was emotional."
Brown added that he hoped his back-room staff would stay in place and thanked the SFA for their help during his tenure.
"I thanked them for their tremendous co-operation," he said.
"There was no pressure on me from the SFA. No-one has said it was time to go. The SFA have been very supportive and there has been no interference.
"I have been with the Scotland team for over 15 years since Alex Ferguson first called me into the coaching team. I have been to every international and five major tournaments.
"They are the best seats in the game and I have had a contribution. It is a wrench."
Top-class coach
Brown refused to sit in judgement of his own performance as Scotland manager but said: "In terms of team spirit, harmony and results we've been a success. We've lost nine competitive matches."
Brown revealed he would be happy to help choose a successor - if asked. "I'd give my opinion if they want it, for what it's worth," he continued.
"But it's one for the executive committee and the chief executive to make that decision."
Immediately following Brown's announcement, SFA chief executive David Taylor expressed his gratitude to Brown for his work over the past eight years.
Taylor said the SFA would now pursue the job of finding an appropriate replacement for Brown.
He admitted the search would take some time and that the difficulty of attracting a top-class coach was something the SFA was aware of.
He said that the SFA was prepared to offer an attractive salary to bring a suitable manager into the job.