The group consisting of 10 officers and 67 soldiers was arrested at the Ataturk international airport in Istanbul.
During interrogation, they said they mistook the coup attempt for a training exercise.
"Only when people started to climb the tanks did we realize what was really going on," one of the detainees was quoted as saying by the newspaper.
According to the soldiers, the colonel, who was in command, ordered to step back when police units arrived.
Turkish President Recep Tayyip Erdogan early in the morning on July 16 declared he is in control of the country.
Prime Minister Binali Yildirim said that all coup supporters were identified and would be apprehended as the country was returning to normal life.
Over 180 people were killed and 1,470 were injured during the events, while nearly 3,000 people have already been detained, according to the prime minister.