The Greece defender has commenced pre-season training after Euro 2012 and he told the Weser Kurier that he has his sights set on a top-four finish this season.
"This year, we have really got to qualify for the Europa League, but in my opinion, Werder should be playing in the Champions League, at least given its history," he said.
Bremen finished ninth last season, six points adrift of a place in the Europa League and they lost top goalscorer Claudio Pizarro to Bayern Munich this summer, signing Nils Petersen as a replacement.
Tim Wiese, Marko Marin and Markus Rosenberg have also left the club and there were fears Papastathopoulos would follow, but the 24-year-old says he is still happy to stay at the club, just as long as his ambitions are matched.
"I will certainly be staying in Bremen this year and I will do my bit for the team," he added.
"But I cannot yet say what happens next year."