Turan was unable to spark Turkey into life as an attacking force, with the Barcelona player withdrawn by coach Fatih Terim in the 65th minute.
"First of all I have to apologise because of my poor performance today. I think I played bad," he told TRT.
"My team-mates gave everything they could. Croatia is a nice team. We could draw but it just didn't happen. We'll do our best.
"The tournament isn't finished yet. But we have to pull ourselves together after this defeat. I hope we can perform better in Nice against Spain. We won't give up. We are in a tough group."
Hakan Calhanoglu called for the Turkey squad to quickly pick themselves up ahead of Friday's clash with reigning champions Spain in Nice.
"We are very disappointed with the goal we conceded," he said.
"We started well. Both sides had their chances but they were better on crosses. [Goalkeeper] Volkan [Babacan] didn't see the moment when Modric kicked the ball when he conceded it.
"It's very unpleasant to lose obviously but we won't give up. We have two remaining games. We should concentrate ourselves quickly."