There could hardly be a more thrilling introduction to global football for the 17-year-old who was thrown on by manager Chris Coleman in the second half as Wales struggled to secure the victory essential to keeping their hopes of qualifying alive.
Southgate was asked about Woodburn over the weekend and wished the youngster well for the future and claimed that simply capping players for the objective of locking in their allegiance was not the way forward for the Three Lions.
Woodburn's appearance was his first for Wales and boss Chris Coleman has refuted the suggestion he put Woodburn on in Cardiff to stop any chance of England persuading the youngster to defect to them.
"I know England were after him for a couple of years but he is so passionate about being Welsh", Rush told Radio 5 Live.
"The manager said to me before I went on to enjoy myself and help the team as best as I could, and hopefully I did that".
Upon making his senior team debut for the Reds last November against Sunderland, the Liverpool Academy graduate became the club's third youngest player in history to do so.
"You never know with young players how it's going to fall", Coleman said. I would never do that.
They were four points adrift of Serbia and the Republic of Ireland coming into Saturday's game, but finished the day just two points behind Ireland, who could only manage a lacklustre draw with Georgia.
"I put him on to add something to us, and he certainly did that".
"20-25 minutes to go, still 0-0, but we have a strong bench - it is a great game for young Ben Woodburn to make his debut because they don't come much tougher than that with that much pressure".
"He probably won't start on Tuesday (against Moldova) but if he comes on he will do a job".