Liverpool right-back Alexander-Arnold limped off late in the second half after injuring his thigh 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 as he awaited tests on Alexander-Arnold over the next 24 hours.
"We're going to have a look. It's not good 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 were rested
Unable to call on players from Chelsea, Manchester City and Manchester United following their European finals, Southgate sent out an experimental team.
It was 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.
"It's an amazing feeling for me, probably the biggest moment of my career," Saka said.
At the age of 17 years and 338 days, Jude Bellingham became the youngest player to start for England since Wayne Rooney in 2003, when he appeared against Liechtenstein aged 17 years and 321 days.
Bellingham was making his first England start after an impressive debut season with Borussia Dortmund, but the midfielder struggled to make his presence felt in an anonymous display.
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 crowds loudly booed the England players when they took the knee in solidarity with the Black Lives Matter movement before kick-off.