After midfielder Joahar Mnari gave them a shock lead in the eighth minute, the North Africans repelled everything Spain threw at them until Raul finally scored with 20 minutes left.
"Spain have an excellent attack but it still took them 70 minutes to score against us," Frenchman Lemerre told reporters.
"We played at an excellent level but we were made to pay a heavy price for a lack of vigilance. We had a plan and it worked for a long time but in the end we were not watchful enough."
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Fernando Torres, a handful throughout the match, scored twice including a penalty to put Spain top of the group and through to the last 16 after two straight victories.
"We were overrun when Spain scored, they began to go faster and we lost our shape," said Lemerre. "But up until then we pushed Spain to the limit."