The decision to award it to the Blues midfielder was announced today by the Dubious Goals Committee.
The goal had originally been recorded as an own goal by Peterborough keeper Robert Olejnik. However the DGC decided that Elliott's 28th minute free-kick was heading into the the net, prior to it skimming off Olejnik's fist, as he attempted to punch the ball clear.
It means that Elliott has now scored twice this season, having previously found the back of the net in Blues' 5-1 demolition of Barnet earlier in the season in the Capital One Cup.
The Dubious Goals Committee is made up of three former football players or football officials, which adjudicates in any instance where the identity of the scorer of a goal is disputed.