The Three Lions took the lead through Harry Kane on 11 minutes but were made to pay for numerous missed chances when a contentious penalty decision saw Ferjani Sassi draw the Eagles of Carthage level on 35 minutes.
Just as it looked like England would be forced to share the spoils in Volgograd, captain Kane nodded home from Harry Maguire's flick-on in injury time to seal all three points in the Group G clash.
"I was happy of the way we kept playing even though the clock was running down," Southgate told BBC Sport. "We stayed patient, we didn't just throw the ball in the box. We deserved the win.
"We created so many clear cut chances, especially in the first half, and were in total control in the second half. We were strong on set plays all night. Even if we had drawn, we'd have been proud of the performance.
"We'll do well to make as many chances in a game again in this tournament. The movement, pace, control from the back with the ball was pleasing. We wore them down. Good teams score late goals – if you dominate the ball like that the opposition tire.
"It's difficult to highlight individuals as it was a collective performance. The squad have been brilliant. We got this result over the last three weeks, not just tonight. That's from everyone who worked so hard together."
England play Panama, who lost 3-0 to Belgium earlier on Monday, in their next Group G game on Sunday.