But City pulled a goal back through Clinton Morrison who rattled in his sixth of the season before Leon Best fired home deep into injury time to claim the draw for Coventry.
It was a demoralising moment for Southgate and his side with the disappointment of their 5-0 home drubbing against West Brom last weekend still raw in the memory.
And Southgate admitted the disappointment of the draw provided the same kind of dejection in the aftermath to last weekend's reverse.
"The feeling in the dressing room is similar to last weekend. In fact, it might be a little bit worse because we had three points in our grasp and we threw them away - that is difficult to take," he said.
"We talked at half time about getting the third goal because you know that if it goes to 2-1, there can always be a ball in your box that causes you a problem - and that's what happened.
"In ordinary circumstances, coming here and getting a point would be a good result - but not when you have a two-goal lead."
Boro looked in determined mood in the opened period and could have the lead inside 50 seconds but Keiren Westwood made a good save from Marvin Emnes.
City themselves had chances - through Best and Morrison - but it was Middlesbrough who looked the most likely and they took the lead in the 40th minute.
Adam Johnson fired in a corner and St Ledger did well to rise above everyone to head into the roof of the net.
That would have been a good end to the period for Boro but it got even better as Williams shot home after Gary O'Neil's cross.
Coventry changed their formation in the second half and they started to come into the game as the match wore on.
Morrison was in the right place at the right time as Best helped on Jordan Clarke's cross and the striker fired home 12 minutes from time.
Southgate felt Stephen Wright should have seen red for a late foul on Leroy Lita but instead it was just a yellow.
And, in the extra minute added for that booking, Best scored at the back post from yet another ball in the box from Coventry to send the home crowd into raptures.
Coventry manager Chris Coleman said: "I've been in the other dug out when that happens and it rips your heart out. You can't describe it. When it comes so late it can feel like a win rather than a draw.
"We had been booed off at half time and to be honest, I would have been booing because we stood off them and were two goals down and could have been more."