Griezmann’s brace took him to 41 international goals for France, same as Platini, and is now only behind Olivier Giroud and Thierry Henry on Les Bleus’ all-time top scorers list.
France have extended their lead at the top of Group D by five more points over second placed Ukraine, who have played a game less.
"It's a great source of pride," Griezmann told TF1 of matching Platini's record for the national team.
"Since I've been here, since 2014, I always try to bring the best, whether it's goals, with my defensive or offensive work."
France’s win ended a five-game winless streak stretching back to their disappointing EURO 2020 campaign.
"We wanted this victory, to show that we were solid and that we didn't lose everything," he added.
"There was a good state of mind. We gave everything we had on the field and we tried to hurt them up front.
"What changed? Maybe we found a system that suits us better. We'll see, the coach will decide. But this time we were strong. We had drawn five times, and it was starting to take a long time. Here, we won in style."
