Liverpool defender Alexander-Arnold was left out of the England squad that drew 3-3 with Germany on Monday, with Reece James starting and Trippier on the bench.
Alexander-Arnold has made just one international appearance in 2022, casting doubt over his place in Southgate's plans ahead of the World Cup in Qatar.
"The other night (against Italy), we didn't need the left back cover," Southgate told reporters.
"Against Germany we did because of the way we went with the team so we needed Chilly (Ben Chilwell) on the bench and we had Kieran who, at the moment, I feel his all-round game is ahead (of Alexander-Arnold)."
Southgate also said that central defender Harry Maguire needs to play regularly for Manchester United ahead of the World Cup. Maguire has not started United's last four league games.
"Why do we pick him? Because he's one of the players who gives us the best chance of winning," Southgate said. "So, really, we should all be wanting a Harry Maguire that's playing regularly and playing with confidence.
"That applies to, of course, quite a few players but he's the one that everything lands on, which must be a tough space for him, really, but he's showing tremendous character."
England begin their campaign in Qatar on November 21 against Iran in Group B.
