Austria coach's future unclear after crushing
"When you lose games and not win them then you go," Constantini told reporters following the heavy defeat in Gelsenkirchen.
"That is how it is in Austria, in Germany and anywhere else. That is part of the game."
Asked whether he would still be in charge on Tuesday in their qualifier against Turkey in Vienna, he said: "That is a possibility. If the [federation president] does not fire me, it could be."
Constantini has been in charge since March 2009 having replaced Karel Brueckner, who lasted only eight months in the job.
Austria have never qualified for a European championship finals only taking part in the tournament in 2008 when they co-hosted the finals with Switzerland and got an automatic place.
They have again all but lost out on advancing to the tournament, lying in fourth place in Group A on seven points after two wins, one draw and four defeats with Turkey second on 13 and Belgium on 12 having played one more game.
Germany have already qualified top of the group after winning all eight of their opening games.