The Germany international made the switch to England in the final days of the transfer window this summer.
"I'm not yet properly acclimatised," Sky Sports News quotes Mertesacker as saying. "Sometimes it feels like an extended holiday.
"It doesn't yet feel like home, I don't have my own house or flat and there's a lack of anchor points like I had in Germany. I still have communications but given the circumstances this is inevitable."
The 27-year-old went on to praise manager Arsene Wenger, who has been suffering from criticism after the Gunners poor start to the Premier League season.
"Wenger has been the pride of arsenal for years, he does not sign players of whom he is not totally convinced," he added. "For Arsenal fans Wenger is a hero and he cannot lose this status."
Arsenal host Sunderland after the international break on October 16.