Barcelona were unable to cope against the high-pressing game of Frank de Boer's side and found themselves 2-0 down at half-time in their UEFA Champions League Group H clash on Tuesday through goals from Thulani Serero and Danny Hoesen.
A second-half comeback began when Joel Veltman was dismissed for a challenge on Neymar inside the penalty area and Xavi netted from the spot, but Barca were unable to find a second goal.
The defeat sees the Catalan side's lead at the top of the group cut to two points and was the club's first loss since being dumped out of the Champions League by eventual winners Bayern Munich in May, with Martino determined his players will learn from their mistakes.
"We lacked intensity in the first half, the difference with Ajax was too big," said the Barca coach. "We should talk about what happened.
"This team is the first to be self-critical. We need to learn from these mistakes.
"We pressed well in the first half, but we lost all duels due to lack of intensity. In the Champions League, you have to be intense for 90 minutes.
"We can't repeat a first half like this one. In the knockout stage, you can be out after a half like that."
Barca will guarantee top spot in the group with a point against Celtic at Camp Nou in their final game of Group H next month.
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