The centre-back revealed he was joining the French champions, though it was unclear whether PSG would pay the reported €20million fee Inter wanted for the defender to move this month.
Skriniar was left out of Inter's squad for the Coppa Italia quarter-final against Atalanta but Marotta stated the Slovakia international will stay in Milan for the rest of his contract before joining PSG.
"There are dynamics whereby players frequently change their shirts," Marotta said. "We have to get used to this kind of football.
"It's not what we like, it's not what the fans like, but we compare ourselves with professionals.
"Skriniar made a choice that falls within his rights, we have a duty to respect it.
"We're certain that he will continue to demonstrate the same professionalism and seriousness that he always has in all the months to come before the season is over, and that he's up to the task of continuing to represent this shirt."