Southgate later took a team meeting with his arm in a sling - and insisted there will be no more jumping for joy like he did after Harry Kane's late victor against Tunisia on Monday night.
"I might not be celebrating any goals as athletically in future", he said.
"We are lucky we have a top-class medical team around us, so it was fine", Southgate said.
Southgate's injury is the second incident of a dislocated shoulder becoming a major talking point in recent weeks after Mohamed Salah suffered a similar problem in Liverpool's Champions League final defeat by Real Madrid at the end of May.
He went to a nearby hospital with FA team doctor Rob Chakraverty for treatment. "I had brilliant help from them, and I am just sorry that I managed to ruin their day off".
Southgate has revealed that he dislocated his right shoulder while jogging on Wednesday afternoon, meaning he will not be able to celebrate England goals with as much vigour as his reaction to Harry Kane's late victor over Tunisia on Monday night.
"For someone to do that and try to help me as a young player says a lot about the person". In fact, he was back at the base for a team meeting and conducted proceedings with his arm in a sling.
"They were a bit surprised in the team meeting and were asking 'what have you been doing?'". It just takes time to realise what situations I get put in and how to adapt to those and be more aggressive. Here's hoping to no further injuries in the England camp.
But he is already the beneficiary of the 32-year-old's wisdom and experience as he prepares to face Panama in Nizhny Novgorod on Sunday.