Turan had already been heavily criticised after Turkey's defeat against Croatia on matchday one and he again failed to impress when his nation locked horns with the reigning European champions.
The midfielder was booed each time he got the ball late in the second half and had to be consoled by Barcelona team-mate Andres Iniesta after the final whistle.
"It was not good to see Arda being booed. No coach wants to see something like that," Terim said at a media conference.
"He is one of our most important players. The expectations were very high, but this should never happen. Nobody deserves this.
"We have to enjoy ourselves. Obviously the way they treated Arda made an impact on the game. I cannot think of a reason for that kind of behaviour.
"I'm criticising myself for the performance of the players who are not performing well. I called them up. Of course, some of them have not been on top of their game. But I should be the one who is criticised. I included them in the team."
Turkey never looked like causing a surprise against Spain and Terim was full of praise for the title holders, although he was not impressed with his own side's lacklustre outing.
"I congratulate Spain, who are a very important team. They are a special team like I mentioned before," he continued.
"The first 30 minutes were ok, but we didn't play well from there on. Spain are very strong, one of the strongest sides in the tournament. But we conceded two goals after individual mistakes, one of which was unbelievable. You have to take your chances against Spain. You cannot deny Spain if you don’t do that. And you cannot afford to concede like that.
"The game was well balanced, but then we conceded that first goal. And then we fell apart. It was very difficult after conceding that second goal. The third goal was offside.
"I never gave up in my life. But today my team threw in the towel. I have never accepted this and will never accept it. Rest assured I will do whatever is necessary to get back on track. I am deeply upset."