Croatia, who are level on 16 points from six games with leaders Belgium, will be without suspended playmaker Luka Modric and defender Vedran Corluka for the game but are still favourites to beat the bottom-of-the-table Scots.
"This is a critical time in the qualifiers and one of which we have no fond memories because my two of my predecessors failed to qualify for major events in the past after slip-ups in June," Stimac told a news conference on Tuesday.
The Croatians have reached seven of nine major tournaments, either European championships or World Cups, since they gained independence from the former Yugoslavia in 1991.
They failed to qualify for Euro 2000 in Netherlands and Belgium under Miroslav Blazevic and the 2010 World Cup in South Africa with Slaven Bilic at the helm.
A 2-2 draw at home to Ukraine in June 2009 ruined Croatia's chances of reaching the 2010 World Cup, while a 1-1 draw in June 1999 against Macedonia damaged their chances of qualifying for Euro 2000.
While Scotland are already out of the running with just two points from six games, Stimac was not expecting an easy ride.
"We have also not beaten Scotland in three meetings so far and there is little doubt they are coming here devoid of any pressure to get a result but determined to stage an upset, which would give them a chance to avoid being among the bottom-seeded teams in future qualifying campaigns," he said.
"Hence we have to stay fully focused in order to take the three points many of our fans have chalked up already, which is what makes games like this very difficult."
Stimac, who took over from Bilic after Croatia's exit from a tough Euro 2012 group including eventual winners Spain and finalists Italy, acknowledged he had plenty of players to choose from to replace Modric and Corluka.
"Gordon Schildenfeld has had a great season with PAOK Salonika and will definitely start at the back, while a plethora of players, led by Milan Badelj and Mateo Kovacic, can stand in for Modric," he said.