But Southgate was unhappy at the penalty awarded by referee Steve Bennett for alleged handball by Luke Young which allowed Villa skipper Gareth Barry to score a fortuitous second-half equaliser. Stewart Downing had given Boro the lead.
Southgate said: "We are maintaining our policy about not complaining about referees but I do question whether it is helping us.
"I have seen the incident again and our lad (Luke Young) has got his back to the play. The shot is hit from only a couple of yards away and I don't see the handball is anything but involuntary.
"I'm bitterly disappointed for my players because we've done so well tonight. Yes, we should have wrapped the game up with a couple of chances we had but we are fighting for our lives and the penalty was a very difficult decision to take."
Southgate admitted: "We have to win back some pride after the Cup game. I said we couldn't guarantee a result at Villa but we could guarantee the right attitude and right type of performance.
"We have gone a tiny step to regaining some of the respect we lost from our fans the other day.
"We have still got a long way to go but it was an important point.
"With the way we played, I felt we deserved more because even though we tired a bit in the second half, Villa didn't create many chances.
"We had the better opportunities and defended very well as a team."
Villa manager Martin O'Neill was at a loss to explain his team's inept performance after they had performed so well at Arsenal in the previous game.
He said: "We didn't play well. We played very poorly and it was particularly disappointing in the first half. If was 40 minutes before we had a shot on goal.
"I felt beforehand we were ready for the game but things never materialised for us. While there was some improvement in the second half, we did not put Middlesbrough under enough pressure all evening.
"We didn't create enough and that was the biggest disappointment. I am very disappointed, this was an opportunity to stay with the bunch and we didn't take it.
"We were very flat and we stayed flat for so long. And normally we can pull ourselves around and anyone who saw us play at Arsenal would not believe this was the same side basically.
"Middlesbrough played very well and caused us plenty of problems but if we are going to be contesting this, we have to win games when we are not playing at our best."