The English Football Association confirmed in a statement that the 23-year-old will return to Merseyside to "undergo further diagnosis on the issue with Liverpool's medical team" after suffering what the player fears is a serious setback in the England squad's final session before Thursday's international friendly against the Republic of Ireland.
"I can't tell you how serious it is because he's yet to have scans," Southgate said.
"What was upsetting was to see him in a fair bit of pain. The fact was there was nobody around him when the injury happened. I didn't like that element of it.
"We just have to wait and see what the scans show. We are all hopeful for him that it's not what it might be. It's not a good situation. I don't see him being involved in the games with us, that's for sure.
"We can't speculate on the exact nature of the injury. It's not possible until we've seen scans. My immediate thoughts are with him because he has had some difficulty with injury in the past.
"We are hoping as much as we possibly can and praying that it's not going to be a long-term one but we'll just have to see."
Southgate bemoaned the lack of collective thinking in approaching revisions to the 2020-21 football calendar in light of the coronavirus pandemic.
Despite the Premier League finishing at the end of July and UEFA's Champions League and Europa League competitions running deep into August, no fixtures have been lost and instead matches are being condensed into a shorter period to realign the game in time for next summer's delayed Euro 2020 finals.
And Southgate said: "Joe [is] a good example. We know the load he's had in the last six weeks so we gave him and the lads who'd been involved in European matches an extra day's recovery. And yet still something like this has happened. There are lots of discussions about extra subs and things like that.
"But the bigger picture here is that governing bodies, broader authorities need to work together. We have a winter World Cup in two years. There was an opportunity this year to think differently. The pandemic has thrown up all sorts of difficulties. But everybody's tried to cram the program into a smaller period and nobody has given way and people haven't collaborated enough.
"We are going to see injuries and it's a desperately sad situation because when you see the impact on an individual, it hits home even more. We're now trying to affect things too late. A lot of these discussions could have happened in the summer. We could have delayed the start of the league, we could have delayed international football. We could have adjusted the calendar in it's entirety and all worked together. And people haven't done that."
The build-up to England's game against Ireland has been overshadowed by the resignation of FA chairman Greg Clarke following comments he made during a Department of Digital, Culture, Media and Sport select committee hearing.
The 63-year-old referred to "coloured footballers", stereotyped south Asians and Afro-Carribean people as possessing "different career interests" and described homosexuality as a "life choice" during a hearing designed to examine why the game had collectively failed to agree a financial rescue package for the lower leagues.
And Southgate revealed he opted to address his squad in light of Clarke's comments while also seeking to defend the reputation of the FA in relation to their efforts to modernise.
"I felt it necessary. I'd spoken to them the day before about the diversity code and the work that had been going on. Obviously, Tyrone [Mings] has been involved in the work behind the scenes. As has Jordan Henderson and Harry Kane," Southgate said "And, so we had spoken positively about that the day before and I then felt it was necessary to explain that what had happened yesterday wasn't acceptable and didn't represent what we stand for as a team and isn't a fair reflection of the FA. People have a view of the FA and those of you who I know have a bit more insight into over 800 people that work at the FA, across that spectrum, there are people from numerous national backgrounds, from different sexuality, members of the lesbian and gay community. It's as diverse and organisation as I've ever been a part of.
"As he said himself, the terminology he used in in a number of areas was not acceptable and doesn't reflect the view of the FA, doesn't reflect what we as a team stand for.
"I don't think he had any alternative but to take the decision he did to resign. I have to caveat that a little bit. I think [with] Greg, what's a shame for him in particular is that he's done a lot of work behind the scenes to support the diversity code, to make a lot of inroads into relationships around Europe.
"I must say that there are often a lot of names put forward and it's easy in the background to have opinions on things without having any responsibility.
"What I admire about somebody like [current FA Inclusion Advisory Board chairman] Paul Elliott is that he's committed himself to football administration. There are a lot of hours to that, there are a lot of meetings to attend that a lot of people don't want to do.
"So the reforms that Paul has helped to put in place over the last few years or over the last few months rather, deserve a lot of commendation.
"I don't know if Paul's the right person for the main role. That's not a decision for me. But I'm just pointing out the type of challenges that football administrators have to have and the type of qualities they have to have."