The defender claimed Arsene Wenger's new-look side was always going to take time to gel and backed the Frenchman to turn their fortunes around.
The Germany international was one of several new faces brought in towards the end of the transfer window.
"I've only been gone a month from Germany. I have not yet properly acclimatised," he said in an interview with the German Football Association website, www.dfb.de.
"Sometimes it feels like an extended holiday. Only slowly am I starting to get used to the fact that the centre of my life is now actually in London.
"I have been living in England since the middle of September, but it doesn't yet feel like home. I don't have my own house or my own flat. There is a lack of anchor points which I already had in Germany. But that takes time, it's normal.
"We have many new players, but I feel that we have integrated very quickly. I still have communication problems, but given the circumstances this is inevitable."
Arsenal have lost four of their opening seven Barclays Premier League games, with Mertesacker coming in for criticism for some of his performances.
"Arsenal is one of the top teams in the world and the level of the league in general is very high," the defender added.
"But it is clear that mistakes happen. They are almost inevitable in a team which has not yet gelled."
Mertesacker is boosted by the faith Wenger has in his team, though.
"The coach has been the pride of Arsenal for years," he said. "Arsene Wenger does not sign players about whom he is not totally convinced. He gives this feeling to everyone on a daily basis. This knowledge gives me a lot of security.
"He (Wenger) has a huge reputation there and enjoys complete confidence.
"For the Arsenal fans Wenger is a hero and he cannot lose this status. There is no one here who is not certain that the success will return. We have a talented team with a lot of potential lying dormant within us and it's only a matter of time before that comes to the surface."