Celtic crashed out of Europe after a thumping 3-0 defeat by AC Milan in their Champions League Group H clash at Parkhead.
With Ajax beating Barcelona 2-1 at the Amsterdam ArenA, the Scottish champions do not even have the safety net of the Europa League this season.
Brazilian star Kaka put the visitors ahead in the 13th minute when he headed a Valter Birsa corner past Hoops goalkeeper Fraser Forster.
Celtic defender Virgil van Dijk missed a sitter at the start of the second half when he blasted a shot straight at Milan goalkeeper Christian Abbiati, a minute before Rossoneri defender Cristian Zapata made it 2-0 from close range.
Mario Balotelli, in one of his more productive moods, scored a third with a drive on the hour mark to compound the misery of the home side who were made to pay for missing several chances.
Celtic remain bottom of the pool with three points from five games and their final fixture at the Nou Camp next month will be for pride only.