Were the Persians Asian

The Middle East is part of the continent of Asia, so - technically speaking - yes. Persians are very proud of their long and heroic past and of a highly developed culture that goes back to the times of Babylon and the ancient Greeks. In those terms they often feel more closely connected to the ancient Hellenistic culture than to the Arab culture. And of course they would never feel "Asian" in the 'Far East' sense of the Word.