Strachan claimed that Manchester City and Chelsea's physical strength separates them from the Gunners, who moved up to fourth in the table with Saturday's 3-0 win over Burnley.
He told Sky Sports News: "They need to match [their rivals] physically. You see Chelsea in the tunnel and these guys are huge.
"Arsenal's football needs to be spot on because they're not like that. In the big games everyone has to be at their best. Manchester City and Chelsea can get away with a sloppy 10 or 15 minutes, but Arsenal need to be spot on.
"I think if they keep all the good players fit and they start doing something when they play the big games [they can challenge]."
Arsene Wenger's side turn back to European action when they host Anderlecht in the Champions League on Tuesday.