The visitors headed into the encounter at the Stade de France with a clear advantage after a 2-0 success in Kiev on Friday.
But that lead was quickly cancelled out in the first half thanks to strikes from Mamadou Sakho and Karim Benzema.
The situation was even more bleak for the visitors when Yevhen Khacheridi was sent off for a second bookable offence in the 47th minute after bringing down Franck Ribery.
France's incredible turnaround was secured in the 72nd minute when Sakho's effort crossed the line via Oleh Husyev.
Fomenko admitted his side faced a difficult challenge against a France side backed by a partisan home crowd, but believes the situation was made even more difficult by Khacheridi's dismissal.
"I have regrets, first of all on a psychological level," he said. "It was not good, we had to be ready and we were not.
"Our game was organised, but not really in the way I wanted it to be. I warned the players about the need to avoid yellow and red cards.
"But it was difficult. France did not surprise me, this is a very strong team with good players. They played at home and their support was very strong. The players wanted to make them happy."
Fomenko apologised for his side's collapse, but vowed to continue in the job.
"I'm really sorry about the result," he added. "We came so far and this is something positive. I want to continue as coach."
