But the Albion midfielder believes the head coach might have more time to make a tactical imprint ahead of the main event now they have got there.
Ayari is a likely starter for the Swedes as they tackle Group F, starting with a game against Tunisia – the land of his father – in Monterrey Mexico.
Potter has been at work on the training pitch in Dallas, memorably wearing a cowboy hat, and that sort of time with his squad was something he lacked when he first took over on an interim basis during the qualifying phase.
Ayari told The Argus: “It was different because you don’t get as much time.
“You train with your club every day with your team-mates and the coach can implement things easier.
“When Graham came in, he had to make sure everyone knows what they are doing and we are together as a team. That’s the most important thing.
“Maybe it is not as tactical as the Premier League because you just need to win game by game. You couldn’t think far ahead.
“But I think it will be easier now because we get more time.
“At that time (the play-offs) it wasn’t so much about him showing how good he is tactically.
“At that time it was about him showing us that he trusts us, putting the team together and always believing in ourselves.”
Potter is a popular – and, it seems, different – character in Sweden and has embraced the culture and language.
Asked whether the squad work in English or Swedish, Ayari said: “Both. He is trying to speak Swedish and he is doing a good job.
“Everybody understands him.”
Ayari showed an eye for a shot, a progressive pass or a run into the box during his time playing for Fabian Hurzeler at Albion.
The expectation with Sweden will be that he partners the more defensively-minded Jesper Karlstrom from Udinese in the engine room.
Ayari said: “He has asked me to play the way I like to play, because I’m me and I’m at my best when I play free.”
The Ayari family are already off to a solid start in the World Cup.
His mum is Moroccan, so saw her nation impress in a draw with Brazil.
But something will have to give in Monterrey in the early hours of Monday our time (the game is a 3am kick-off BST).
Ayari could have been playing for Tunisia but opting for Sweden was not a difficult choice.
He said: “It was kind of easy for me, because I was born in Sweden and came through the national teams when I was younger, so it was a simple decision.
“Obviously, I want the best for them. My mother and father are from those countries.
“When I was younger I was there a lot for holidays and stuff.”
