Arsenal have improved defensively under Mikel Arteta, but ahead of the international break, they were exposed by Aston Villa, who beat them 3-0 at the Emirates.
Parker is of the view that the Arsenal defenders still do not think defensively and fail to identify the gaps in the team when they develop during a game.
He believes David Luiz symbolises everything wrong with the Arsenal defence as the Brazilian still lacks the focus and the single-mindedness needed to play at the heart of their defence.
The former Leeds star feels as a unit Arsenal still do not defend properly and do not show the kind of determination needed to stop their opponents from scoring goals.
The ex-Leeds defender, looking at how the Whites can exploit the Gunners, said on LUTV: “Down the sides. Get at the back there.
“I don’t think they think defensively, which is kind of silly to say from a defender’s point of view, but they don’t.
“They don’t plug gaps.
“The big example for me is David Luiz – I think he is a very good footballer, but for a defender who wants to defend week-in-week-out, I just think his mind is elsewhere sometimes.
“It just depends on whether he turns up.
“If his mind is on it, yes he is a good player, but as a collective unit, I don’t think they work hard enough to stop the ball from going into the back of the net.
“With our movement and creativity between the lines, we can get at them.”
Leeds are also struggling defensively at the moment and have conceded eight goals in their last two games.