Southgate told the Evening Gazette: "Stewart asked the question two or three weeks ago as to who would take the penalties.
"He made it clear that he wanted to take them and that was fine by me. You need penalty takers who want to step forward to take them.
"Sunday's penalty was a crucial moment for us in many ways.
"If you don't score in those situations then all the old fears come to light again.
"But Stewart showed lots of courage to take it and you could see the huge difference it made to our performance.
"We've not actually sat down and stipulated who will take penalties but if Stewart wants to stick with the job then that's fine by me."