RELATED: What Would Have Happened If Obi-Wan Was The One To Arrest Palpatine? Nonetheless he took such necessary action as he genuinely believed that Palpatine was 'too dangerous to be kept alive,' thus sacrificing himself to end the Sith for good. Such an outcome may even be foreseen by Mace beforehand.
The Jedi had long been doubted or even criticized as some form of religious group dominating galactic politics with little restraint, and such a shocking turn of events would most likely call for Mace Windu to be brought to justice, particularly since 'Chancellor Palpatine' had quite a lot of supporters in the Senate. Having killed such a widely known and prestigious public figure (since almost everyone in the galaxy knew Palpatine as Chancellor of the Republic), there would certainly be widespread shock and public outcry.