GOAL - Seth Vertelney
France head coach Didier Deschamps opted for a 4-4-2 shape rather than his usual 4-2-3-1 formation, and France struggled to adjust to the change.
Griezmann opened the scoring in the 19th minute with a curled effort but France were unable to find a killer second goal. Les Bleus were punished in the second half, as Presnel Kimpembe's own goal gave Ukraine a point in both teams' qualifying opener.
Speaking to TF1, Griezmann said: "We needed maybe more offensive players who are able to go one-v-one on the sidelines. We will learn to play in a system like that and try to start winning again. We wanted to win but we didn't play a great game. We're going to look at it all and try to improve."
Deschamps said: "We should have secured the win in the first half, we had the opportunities. It was more difficult in the second half.
"The goal that we conceded was avoidable, we pushed to the end. We are obviously disappointed, it would have been ideal to win.
"The result proves that Ukraine is a good team. We lacked energy in the second half. We can do better. It is not necessarily a match where we were going to create a lot of chances. We needed more precision and movement."
Following Wednesday's match, France will face Kazakhstan on Sunday and then Bosnia and Herzegovina next Wednesday.
The matches represent the last chance for players to impress Deschamps before he names his roster for this summer's rescheduled Euro 2020 tournament.