Stewart Downing had the chance to give Boro the lead but missed from the penalty spot before Turkey international Tuncay secured the win for Boro with a goal five minutes from time.
"It was a hard-fought victory, and we made hard work of it," Southgate said after the match at the Riverside.
"We should have had it wrapped up long before we actually did. We need to be more ruthless in both boxes.
"The penalty was a bit of a turning point. At 2-0 they would have been dead and buried.
"The pleasing thing is that we kept our nerve and Tuncay came up with a great finish to give us the win."