"I enjoyed my debut in front of so many spectators, but am disappointed we did not get the result," he said.
"I think it was not so much of a problem for me on the pitch, but Sunderland played very defensively. All of their players stayed in the box. It was very difficult for us.
"We tried to play for a goal and had chances, but we were not happy."
Arshavin - signed from Zenit St Petersburg on transfer deadline day - feels it will not be too long before he is fully up to the pace of the English game.
"I am doing everything I can to be fully fit as soon as possible," said the Russian, who is ineligible for the remainder of the Champions League this season.