The 'Gunners' were stunned by a fightback from the North East club as they secured victory at home on Sunday afternoon.
Vidic gave his verdict on the match to 'Sky Sports', noting that a lack of communication was to the detriment of Arsenal as they struggled to defend well on Sunday.
He said: ''I think there is a lack of communication, they are watching the ball and not reacting. There are six players against three and there is no communication about who is going to go and attack the ball.''
The former Manchester United defender added: ''It seems like in this situation, it is definitely organisation [issues]. I think communication is the key. Everyone is watching what the other player is going to do, no one is saying ''you attack, I'll go behind''.
Going forward, he warned: ''They have to defend. For me, when Arsenal get to pre-season, they don't have to think about scoring goals, they need to think about keeping a clean sheet.''
He added that the pressure is piling on for the North London club: ''I said two weeks ago, Burnley are only two points behind Arsenal and people were like, 'Come on, relax'. No, I can't relax because they really are two points behind Arsenal.''