The switch to a back three for the first time in three years gave Southgate the opportunity to select Alexander-Arnold as a wing-back, after some underwhelming performances from the Liverpool star in midfield.
But Southgate resisted the temptation to play the creative and technical 25-year-old against Switzerland, instead moving Newcastle United’s Trippier from the left to the right.
Trippier has attracted criticism for his performances on the left and while he would be more at home on the right, Carragher still believes it was a mistake not to play Alexander-Arnold.
Other changes in England saw Aston Villa’s Ezri Konsa come in for suspended Crystal Palace centre-back Marc Guehi, with Bukayo Saka filling in at left-back and Phil Foden retaining his spot despite a low-key tournament.
“Kieran Tripper has done a good job on the left but they chose him over Trent Alexander-Arnold (at right-back) which I can’t understand at all,” Carragher told Sky Sports.
“It’s not the Liverpool fan in me, I’ve long believed that Kyle Walker is right to play right-back for England, I think Gareth is experimenting with Trent in midfield because he has world-class ability on the ball, but not enough.
‘But the reason you play Trippier over Trent I just can’t get my head around. The only reason is that Kieran is playing some other games, maybe he believes.
“But if you think about it defensively, the whole point of playing three at the back is to get off the wings and you have Kyle Walker, the fastest player in the squad to burn anything if you get caught.
“So, to not put Trent in that position, I can’t believe it, to be honest. I can only imagine where his head is right now.
“I think after this tournament, Trent Alexander-Arnold should start for England, whether it’s in the back four or the back five. He’s a very good player.
‘Trent has got world-class ability, Kieran Trippier is just a fantastic player who, at times, has had a very difficult season for Newcastle.
“He’s done for England, but to play before Trent, I don’t see it. Trent has world-class ability, so I think I like Trent.’
England are bidding to reach the semi-finals of the European Championship, three years since they were knocked out as finalists at Euro 2020.
But the Three Lions have been underwhelmed in Germany and face a Swiss team that beat defending champions Italy last time out.
Southgate gave Trippier huge credit in his pre-match press conference, insisting he had done a ‘great job’ for the team.
“Kieran Trippier has been outstanding for us,” he said. ‘Luke is available, he is available to start but Kieran has also done a great job for the team.
“He obviously doesn’t give us the balance that his left foot gives us, but his leadership, his communication, his talk – just ask the players he’s playing – it’s phenomenal and it helps his game.
‘Low quality and slightly arty to die for. You can never have enough good speakers on the pitch and he has incredible quality in the area as well as quality on the ball.
‘He adapted and did a good, good job for us.’
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