The Frenchman also said PSG defender Marquinhos pushed him during the incident at the Parc des Princes.
"I'd already been booked so didn't want to make trouble. I made a small challenge on Verratti but he threw himself on to the ground," Giroud said.
"I didn't understand, so I asked him: 'What are you doing? Then he got up quickly and Marquinhos pushed me from behind. I don't know how Verratti fell over a second time."
"I didn't go looking for trouble so it's frustrating. I think that the referee was tricked. Verratti was also on a yellow, so I was surprised by his behaviour," Giroud added.
The France striker will miss Arsenal's next Group A game at home to FC Basel on Sept. 28, while Verratti will be sidelined for PSG's match away to Bulgarian champions Ludogorets.
(Reporting by Ian Rodricks in Bengaluru; editing by Ken Ferris)
