The Crescent Stars needed to win their final group game against the Netherlands to reach the World Cup play-offs but were defeated and instead finished fourth
The Group D competitors needed to overcome the unbeaten Dutch to guarantee a spot in the Uefa play-offs but goals from Bayern Munich forward Arjen Robben and Galatasaray midfielder Wesley Sniejder denied them even a point in their final game.
Terim was apologetic for the Crescent Stars' failure to reach their third-ever World Cup but was realistic about his side's quality in comparison to Louis van Gaal's men.
"First of all, I must thank our supporters," he told NTV-Spor. "They came here and the stadium was full. We are sorry for the Turkish public.
"It would have been a pleasure to have achieved qualification. But we should tell the truth: the Dutch are better than us and they play good football. You must score to beat these kinds of teams.
"If we could have got to 1-1, then everything could have been different. But it just didn't happpen.
"My players tried to achieve what was almost impossible. I'm very sorry. We wanted it so much but sometimes that's just not enough."
Romania defeated Estonia 2-0 to finish second in Group D and grab the play-off spot with Hungary leapfrogging the Turks by beating Andorra 2-0 in their final game, consigning Turkey to fourth.