The Albion midfielder is eyeing a World Cup qualifying play-off final at home to Poland on Tuesday after clearing the penultimate hurdle.
Ayari played the first 77 minutes of the win over Ukraine at Levante’s stadium in Valencia.
He left the action shortly after Sweden had gone 3-0 up on the way to a 3-1 victory.
Sweden secured a play-off spot via their results in the UEFA Nations League rather than in a dismal World Cup qualifying group.
Sidelined recently by a dislocated shoulder, Ayari has been on the bench with his club since returning.
But he was at the heart of the Sweden effort as ex-Albion striker Viktor Gyokeres scored a hat-trick.
Speaking ahead of the game, Ayari said: “It was a tough injury. It's the shoulder so the slightest thing that affects it can make it worse.
“But I'm fine. I'm happy. I'm here.
“It happened recently so I just have it to make sure it doesn't happen again.”
Ayari almost crowned his return to club action with a goal as his volley was blocked by Curtis Jones late in the 2-1 win over Liverpool.
The midfielder was among the players eyed by Nottingham Forest in January as bosses at the City Ground appeared to take a major interest in the Albion squad.
Ayari told Swedish media of the Forest bid: “I'm focusing on Brighton. I feel happy there. From my side, it wasn't something I focused on.
“That's how it is when you're a player. Regardless of the price tag or the club, it doesn't matter. I'm happy where I am and I just have to keep going.”
Potter has made a slow start as Sweden boss in terms of results but was delighted with victory in his first game since agreeing a four-year contract extension.
He said: “Viktor was world class and, when you have players like that, you always have a chance.
“I thought we were tactically good and defended well as a team.”