The Dutch champions were dumped out of European competition altogether after collecting just their second point in Champions League Group D
Rostov sealed Europa League qualification after grinding out a 0-0 draw with PSV Eindhoven in Champions League Group D.
The Russians only needed to avoid defeat against the Dutch champions to stay in Europe after last month's shock 3-2 victory over Bayern Munich in their first-ever Champions League group-stage triumph.
Meanwhile, Tuesday's reverse completed a disappointing campaign for Phillip Cocu's men, who fell far short of the form that took them into the knockout stages of last season's competition.