The Italian midfielder and Giroud came together in extra time of Tuesday night's 1-1 draw at the Parc des Princes and the Arsenal man was left unhappy with how easily Verratti went to ground.
"Being on a yellow card, I didn't want to make waves," Giroud said post-game.
"I obstructed Verratti, he threw himself to the ground and I don't understand. Marquinhos pushed me from behind and I don't know how Verratti falls a second time.
"It escalated the situation. It's frustrating, especially since I don't know if the referee saw what happened.
"I was really surprised at his behaviour."