Arnautovic had an ill-fated spell on-loan at Inter last season.
"I am very happy for the goal that I scored against my former team," Arnautovic said.
"Winning 3-0 against the Champions of Europe is very important.
"This Inter side is different from the one in which I played in, but it's still Inter even with the many absences and we had to do our best to win.
"I am happy to see my friends again and I wish them the best for the Club World Cup.
"Good luck, I hope that they win it."