The Three Lions commenced their group-stage campaign with a 1-0 victory in Gelsenkirchen courtesy of Jude Bellingham's early header.
There were aspects of England's performance that will need improving if they wish to progress to the latter stages of the competition, yet Southgate will be more concerned with collecting three points.
Generally-speaking, it was a positive evening for Southgate and his squad, but an injury concern materalised during the closing stages of the contest.
Trippier - who was being used at left-back - went down on the far side of the pitch, bringing a worried look on Southgate's face given England's known issues in that particular position.
After a period of treatment both on and off the pitch, the Newcastle United defender was able to complete the match, but the short turnaround naturally puts his participation in the next match in some doubt.
What did Southgate say about Trippier injury?
Speaking to talkSPORT after the match, Southgate was quick to play down issues regarding the 33-year-old's fitness, hinting that it was more down to a lack of minutes.
Southgate said: "Just a bit of cramp really. I mean, that's his first 90 minutes in months and to play the way he did just shows what an incredible character he is for us."
Between March 2 and May 11, Trippier missed out on Premier League action due to a calf issue before returning for the final three matches.
While Trippier would play 63 minutes at Manchester United on May 15, he only featured briefly in the two fixtures either side of that game.
Although the versatile full-back was able to play 62 and 64 minutes in warm-up friendlies against Bosnia-Herzegovina and Iceland, he had previously not completed 90 minutes since February 27.
What now for Trippier, England?
England are back in action as soon as Thursday evening when they square off against Denmark in the second of their Group C matches.
Southgate's comments would seem to indicate that Trippier is in contention to start a second successive game, but keeping the veteran fit could prove important as the competition progresses.
First-choice left-back Luke Shaw has not played since February due to injury, while the versatile Joe Gomez is another alternative.
Despite an unchanged back four seemingly likely, either of Shaw or Gomez could be called upon at some stage on Thursday to help manage Trippier's minutes.