I need to disagree. As a (central) European person I very much consider at least Istanbul to be an European city - not sure about the whole of Turkey, though.
After some thoughts why I feel this way I think it boils down to geography and history. Istanbul is geographically on both sides of the bosphorus strait, where the “continents” Europe and Asia are considered divided. And then it has historical significance for Europe (as Constantinople), being one of the major stable forces in Europe during at least the middle ages (but also before and after).
Yeah, they dont. Contradictorily so, since the part of the Turkey that is geographically in Europe is larger than many European states both in respect to surface area and also in respect to population.