The 28-year-old has often seen his performances come under scrutiny since joining the Gunners, with the German having once again come under fire for his showing in the 4-0 defeat to Liverpool.
And former Bayern Munich star Effenberg believes Ozil must step up to the plate, pointing to past comments from Steven Gerrard who has criticised his performances away from home.
Effenberg wrote in his column for t-online : "I have seen matches with Mesut where I say: 'he must do more'. I remember those matches against Bayern in the Champions League. He disappointed many people there - including [Germany manager] Joachim Low.
"Steven Gerrarrd said he would let his team down and be a burden in matches away from home. You can't say he is completely wrong. Ozil has to see and realise that.
"It is not like he is 20 years old and a young player. He turns 29 in October. You wait for an improvement in that area for years. You hoped there would be a development, but it hasn't happen."
Effenberg also discussed Julian Draxler's situation at PSG and believes that he is capable of starring in the same side as the likes of Neymar and Kylian Mbappe.
He added: "If he manages to push through [into the team] at Paris now he will be a world-class player. And that must be his goal. I see him fitting in well at PSG. His development has been great.
"Why shouldn't he play alongside Neymar? Draxler is more mature than Mbappe. And experience is a very important factor."