The Young Lions were trailing in the Euro2017 qualifying fixture before they rallied to score three goals in the last ten minutes of the game.
Sunderland starlet Watmore was involved in all three goals as he won the penalty for James Ward-Prowse's equaliser, scored the second and then provided the assist for Wolves' Arsenal loanee Akpom's injury-time sealer.
"I didn't think for one minute that it was a game we deserved to be behind in, because there was only really one shot on target," Southgate said.
"We'd played extremely well up until the final third and hadn't managed to find that cutting edge.
"So great credit to the boys that came off the bench, they put the disappointment of not starting the game to one side and it was a super contribution which really turned the game for us.
"We knew that we were ending up a little bit narrow and [Watmore's] width would give us a different option and his pace at that stage of the game, because we'd kept the ball so well and knew the opposition would tire.
"It's important to stick to our beliefs and the way that we want to play, but also sometimes you have to go a little bit more direct and mix the game up.
"We got two strikers on the field and started to pose the opposition some different questions.
"So I'm delighted for him, he's a great kid to work with and it's great that he's got his reward tonight."