Boro were sucked into the bottom three for the first time in more than three years after Sunderland's stoppage-time winner against Derby saw them leapfrog their north-east rivals.
But Southgate, who has enjoyed the backing of famously-patient chairman Steve Gibson despite more than three months without a win, refused to be too downcast over the outcome of today's fixtures.
"We've slipped a place today but it was still a very important point for us," he said.
But the manager must take credit for his substitions, which paid off in spectacular fashion when summer signing Tuncay Sanli netted his first goal in English football with an unerring header six minutes from time.
"It's a poor goal that we conceded but at least we had the character to dig in and keep going forward and I think we've got the reward," Southgate added.
"We might have pinched it at the end but I certainly think we were good value for a point."
Despite a lack of quality throughout that largely manifested itself through both sides giving the ball away, there was attacking intent from both teams.
"Both of us want to play attacking football," said Southgate.
"We felt with the personnel we had available, let's have a go at it.
"We just weren't able to add the finishing touch in the first half or that extra bit of quality around the penalty area.
"In the position we're in, we at least gave a performance that was healthy in its endeavour, its character."
He added: "From 1-0 down, yes, but at no other point in the game did I think we were going to lose it.
"I'm not relieved. I'm disappointed we've given ourselves a lead to claw back again."