"Concerning the question of the coach, this matter is not up for discussion," Austrian Football Union chief Leo Windtner said on the governing body's website.
"It doesn't look so good after two such games but, in principle, we stand for continuity and we don't want to start up the team chief discussion after every little set back.
Austria have dropped to fourth in Group A, with seven points from five games, after a 2-0 home defeat by Belgium on Friday and a loss by the same score in Turkey on Tuesday.
They host group leaders Germany, who have 15 points, in their next game at the start of June with a second-place finish their only realistic hope of qualifying for the finals in Poland and Ukraine in 2012.
Austria have never qualified for the European championship finals, only taking part in the tournament in 2008 when they co-hosted the finals with Switzerland and got an automatic place.
Constantini has been in charge since March 2009 having replaced Karel Brueckner, who lasted only eight months in the job.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.