Saying he does not fear a "domino effect" of referendums across the continent, he also expressed his belief that Austria will be able to manage in the aftermath of the British departure from the EU, Xinhua reported.
Fischer nonetheless described the outcome as a "shock" that made Europe "hold its breath".
Austrian Chancellor Christian Kern also expressed disappointment at the outcome of the British referendum, claiming Europe will now lose some of its global standing.
"Today is not a good day for Great Britain, for Europe, and also not a good day for our country," Kern said.
In response to the notion that the British outcome may lead other EU member states to call for similar referendums, Kern said these would "make no sense", and noted that no such referendum would be held in Austria.
He said one must now learn from the result of the British referendum, and "draw very clear conclusions".
This includes paying attention to the concerns of the populace, and the showing of political leadership. He also argued that up to now pro-EU advocates have been "much too defensive".
Meanwhile, the heads of Austrian economic and industrial groups expressed dismay at the outcome of the British referendum on its EU membership, and have called for new ways forward.
President of the Austrian Economic Chambers Christoph Leitl stated the outcome of the vote was "unfortunate". He said the Austrian government and other social partners now have the task of mitigating the negative consequences on Austria.
In addition EU decision-makers must act with "cool heads" as the separation of Britain from the EU takes place, with the phase of uncertainty to be kept as short as possible.
The director of the Austrian Institute of Economic Research Karl Aiginger expressed similar sentiments, noting that while the decisions of the British has led to some uncertainty, it has provided the EU with the chance to implement some long-overdue reforms and measures that could bring back economic growth.
Europe must strategically tackle the issue of economic recovery and not be caught up in the issue of the Greek crisis, or the migrant crisis and "forget everything else", he added.
President of the Federation of Austrian Industries Georg Kapsch said the EU is now required to "provide quick answers for its future viability, to solve the crisis of confidence".