Stewart Downing's well-struck 67th-minute goal looked to have won the Barclays Premier League game for the home side.
It was hard luck on Southgate's men, who had fought their way back from Grant Leadbitter's second-minute opener to lead 2-1 despite losing Tuncay Sanli and former Sunderland favourite Julio Arca to injury before the break and Mido just after it.
Southgate challenged his players at half-time to fight their way through a dreadful run of luck, and could only applaud them for their efforts after Miller's last-gasp intervention denied them all three points.
The former England defender said: "It would be easy to throw things and be annoyed, but I have got to say, I am proud of what the players have done because it was an afternoon where pretty much everything that could have gone against us did.
"We went a goal behind in the first minute to a shot that hit their own player and deflected right into his path, but our response to that was very good, we pulled ourselves back into the game.
"We lost three very influential players to injury and I said to them at half-time, 'You have afternoons like this in football and there are two options. You either sit and feel sorry for yourselves and you lose the game, or you roll your sleeves up and you say right, what a great game this is to win now with everything going against us'.
"Their attitude and the way the responded were fantastic. We looked like we might edge it - we didn't, but I am not prepared for them to leave this ground with their heads down.
"They were very down at the end, but as a manager, you can only ask them to give what they have given.
"They are out on their feet, but we have come out with a point. Yes, we would have loved it to be three and I think we just about deserved it to be three, but we didn't get it and we dust ourselves down and we go again."