Liverpool right-back Alexander-Arnold limped off late in the second half after injuring himself while clearing the ball.
The 22-year-old looked emotional as he needed assistance to hobble around the Riverside Stadium pitch.
Southgate admitted he was concerned over Alexander-Arnold’s chances of making the tournament as he awaited tests over the next 24 hours.
“We’re going to have a look. Clearly it’s not a good sign to see him come off in the way he did,” Southgate said.
“We’ll have to assess him. I think it’s a thigh but the medical team are assessing him.
“It’s not a good sign to see him have to walk off as he did. We’ll know more in 24 to 48 hours.
“We don’t know the full extent. The last thing you want is to see him come off in the way he did.”
Alexander-Arnold, who finished the season in fine form, is one of four right-backs in the England squad after being selected despite reports he would be left out.
Kieran Trippier, another of the right-backs, was used at left-back against Austria, while Reece James and Kyle Walker would also be in contention to start if Alexander-Arnold is ruled out.
Unable to call on players from Chelsea, Manchester City and Manchester United following their European finals, Southgate sent out an experimental team.
It was Bukayo Saka who staked a claim for a place in the starting line-up for their tournament opener against Croatia at Wembley on June 13.
The 19-year-old Arsenal winger was a lively presence on the left flank and capped his eye-catching display with a composed second half finish for his first England goal.
“It’s an amazing feeling for me, probably the biggest moment of my career,” Saka said.
England complete their pre-tournament preparations with a friendly against Romania back in Middlesbrough on Sunday.
Aside from his selection issues, Southgate will be alarmed that a section of the 8,000 crowd loudly booed the England players when they took a knee in solidarity with the Black Lives Matter movement before kick-off.
“I did hear it. It’s not something on behalf of our black players that I wanted to hear, because it feels like a criticism of them,” Southgate said.
“Some people think it is a political gesture that they don’t agree with, but that is not the case. I was pleased it was drowned out with applause.”
Alexander-Arnold had started brightly as he surged onto Harry Kane’s raking pass and forced Daniel Bachmann to tip over his fierce drive.
England lacked a cutting edge in the first half but they carved open the Austrians to take the lead in the 57th minute.
Kane’s pass picked out Jesse Lingard just inside the Austria area and his attempt to find Jack Grealish was diverted to Saka, who had the simple task of slotting into the empty net from close range.
Like Lingard, Ben Godfrey was one of six players left out of England’s final 26-man squad when it was announced on Tuesday.
But Godfrey still came on for his debut and was immediately rescued by his Everton team-mate Jordan Pickford when the England keeper scrambled to kick the defender’s woeful backpass off the line.
Southgate had challenged Lingard to “show me I’m wrong”, but the Manchester United forward was unable to replicate the fine form he showed on loan at West Ham.
Grealish was more impressive as the Villa midfielder offered flashes of his playmaking quality.
“Jack showed some lovely touches. You can see he’s still getting to full fitness, with the bursts you know he can make. He’s a quality player,” Southgate said of Grealish.
#AlexanderArnold #injured #England #beat #Austria #Euro #warmup