During the 2006–07 Super League Greece, Papastathopoulos managed to make 14 appearances whilst competing against the likes of Bruno Cirillo, Traianos Dellas and Vangelis Moras. In AEK Athens' 2006–07 UEFA Champions League campaign, Papastathopoulos managed to play in three out of six group games. In these three games, AEK managed one win (the famous 1–0 victory over A.C. Milan, where he man-marked Filippo Inzaghi), one draw (the 2–2 away draw with Anderlecht) and one loss (the 3–1 away defeat to Lille). During the 2007–08 Super League Greece, he was a mainstay in AEK's defence, keeping out competition from Geraldo Alves. He also played in the 2007–08 Champions League campaign, and in a Super League match, he became AEK's youngest-ever captain, at age 19, in a game against local Athens rivals Panathinaikos in 2008.