Ozil came on as a second-half substitute in Arsenal’s 2-1 loss to Watford at Vicarage Road.
At 1-0, the German had a great chance to double his side’s lead, but saw his tame shot pushed away by Hornets goalkeeper Heurelho Gomes.
Watford equalised within a minute of the miss, Troy Deeney scoring from the penalty spot, before Tom Cleverley netted a late winner.
Savage says a player of Ozil’s quality should have scored and suggests manager Arsene Wenger does not deserve to take flak after the loss.
“I think he should score that, Mesut Ozil,” Savage said on BT Sport.
“People say about his talent but he has to score that.
“The thing was he was so laboured in the way he hit it, he didn’t even go for a corner.
“He’s either got to open his body up and put it in the far corner, or give the goalkeeper the eyes, but he went straight at the goalkeeper!
“That’s a comfortable save, what is he, 16-yards out, just inside the penalty box, and he hit it straight at the goalkeeper.
“Arsenal now, since the defeat to Liverpool, they’ve done okay.
“But now, they’ve gone to Watford and it’s the same old same old.
“Now the manager will get hammered, but saying that the manager will get hammered, but he’s brought on Ozil and he should have wrapped the game up for them.”