The 49-year-old was appointed in the summer following the retirement of Pat Rice, and has been credited with the club's improved defensive performances so far this campaign.
Arsene Wenger's side have conceded seven goals in nine competitive matches, compared to 17 at this point last season, but each of their last five goals have come from either crosses or set pieces.
"It's a blessing and a curse for Steve," Adams told the BBC. "People are going to say 'what a fantastic defence' because he played defence.
"And a goal goes in they're all going to be turning round to him and saying 'come on Steve you're doing a really bad job'.
"My experience of Arsene Wenger is that he's very offensive and it's going to be very difficult for Steve."
Adams played for Arsenal between 1983 and 2002 and won the English first division title on four occasions and the FA Cup thrice.