Terim's side made a horrendous start in their bid to reach Euro 2016 from Group A as Iceland embarrassed them in Reykjavik.
Jon Dadi Bodvarsson, Gylfi Sigurdsson and Kolbeinn Sigthorsson all scored for Iceland, while Turkey had Omer Toprak sent off for a second yellow card in the 59th minute.
Patience among Turkish football fans is not high after three successive failures to make major tournaments.
And although the increase from 16 to 24 teams in the European Championship means they should reach the 2016 tournament in France, this was not a good start.
Terim – who said he was "very much disappointed" with the result, added: "I was worried before the game that the team was not totally ready.
"I congratulate Iceland, they played better than us and we deserved the loss. I hope that such a thing will not happen again.
"If we had not dropped down to 10 men, we might have brought the game to a draw.
"Only players who can cope with this level of football will continue with us. The national team is where you should perform 100 per cent."
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
