Mr Jones, who allowed Sunderland striker Darren Bent's goal to stand even though the ball had hit a beach ball thrown onto the pitch by a Liverpool fan, has been demoted from taking charge of any Premier League match this coming weekend.
The Chester-based official should really have disallowed the goal and re-started the match with a drop ball.
Jones will be the man-in-the-middle for Posh's home match against Scunthorpe United on Saturday afternoon.