Southgate said: "We will maintain our policy of not complaining about referees but I do question whether it is helping us. I have seen the incident again and our lad has got his back to the play.
"The volley is hit from a couple of yards away and it hits Luke Young and, if you are not looking at the ball, I don't see how it can be anything but involuntary handball.
"I am bitterly disappointed for my players because they were outstanding tonight and it was a very difficult decision to take.
"We've got to go through the right channels. It won't do us any good but we will go through the right channels and the pictures are there for everyone to see.
"It doesn't need me or any of my players to comment - and I've told them not to comment. I would think Keith Hackett's phone will be difficult to get through to with everyone else on to him but that's all we can do."