The Group H reverse was Barca's first loss this season in all competitions - and their first under Martino - which cost them a chance to seal the top spot, having already secured their place in the last 16.
A fired-up Ajax, roared on by their vocal fans, took the game to an injury-hit Barca in the first half, harrying and hassling them before taking a deserved 2-0 lead with goals from Thulani Serero and Danny Hoesen.
Although the Spanish champions dominated after Ajax were reduced to 10 men shortly after halftime and pulled a goal back through Xavi's penalty, they struggled against a home defence well drilled by coach and former Barca player Frank de Boer.
"Ajax began with more intensity than us and we paid the price," Martino, who took over from the ailing Tito Vilanova in the close season, said at a news conference.
"The second half was a different story and we played in a way more in tune with what Barca represents. The problems in the first half came more when we had the ball than when we didn't,” the Argentine added.
Barca have another chance to seal the top spot in the group when they host Celtic on Dec. 11. The Scottish champions lost 3-0 at home to AC Milan on Tuesday and are bottom of the group on three points from five games.
Barca have 10, Milan are second on eight and Ajax, whose final game is against the Italians at the San Siro, seven.


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