Stimac has only lost five games as national manager, but four of those have come in the last four months, and defeat in the final Group A qualifier at Hampden Park on Tuesday prompted the former defender to offer his notice.
The 46-year-old watched as Robert Snodgrass and Steven Naismith condemned them to defeat, although their place in the play-offs was already assured.
Stimac was far from impressed and explained that he wanted to give someone else a chance if he did not have the backing of the Croatian football federation (HNS).
"It is a bad defeat," he admitted. "I offered my mandate (resignation) to the president of the Croatian football federation because of the latest results of our team, because everything that surrounds us.
"Never mind that we qualified for the play-offs, I want to show some morale, certain responsibility, and if there is anyone in the federation that does not believe in my work I want to give them the chance to change.
"They will have a meeting to discuss it."
Croatia will be one of the seeded teams for November's play-offs, but it remains to be seen whether Stimac will be in charge.
And he admitted that a change may be what the nation needs after failing to win any of their last four qualification matches, although he feels he was left fighting an uphill battle.
"It is all about the positiveness surrounding the football in our country," he added. "It seems we are not happy in Croatia to qualify for the play-offs.
"We were not happy after the first game even though we beat Macedonia, we were not happy in the second when we drew against Belgium or beating Wales 2-0 - they said it was supposed to be 15-0.
"After Wales we went to Macedonia and beat them 2-1 and they said that was not good because they were on the up. We beat Serbia 2-0 and they said we barely survived and the goalkeeper saved us.
"We beat Wales 2-1 and they said we were lucky. That's how it works in Croatia.
"There were a lot of people against me from the beginning."
The former international - who won 53 caps for his country - took over from Slaven Bilic in July 2012 and has overseen eight wins, two draws and five defeats during his tenure.
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