But the midfielder needed a few moments to join in with the celebratory mood after his side ensured Conference League qualification.
Hinshelwood was part of the squad who tackled the Europa League in the 2023-24 season.
The Conference represents a lower tier than that and was not what the Seagulls were targeting as they went into the last two games of the season.
But they can relish UEFA competition, despite ending with defeats by Leeds and Manchester United.
Hinshelwood said: “The game's a bit different. Maybe it's a bit slower but we've had that experience now and we've been dying to get back and we're delighted because we can play on a Thursday and a Sunday again.
“That's what this club wants and now we get to fulfil that.”
Hinshelwood has experienced European success with England under-21s and is likely to thrive back on the continental stage.
He admitted he was bitterly disappointed by the 3-0 setback against Manchester United and blamed himself for poor marking on the first goal, headed in by Patrick Dorgu.
That disappointment in the stands at the Amex quickly changed to celebration when eighth place was secured by Brentford’s draw at Liverpool.
But Albion’s No.13 found it rather harder to change gear mentally.
Asked soon after the game whether anyone had told him to cheer up for the post-match lap, he said: “Yes, a few!
“I'm still not fully over it because we had a massive opportunity.
“But, look, we'll take it. I think, when you're reflecting on the season, if you had said that we would finish eighth and get into Europe after that Palace game (losing 1-0 at home in early February), then we would have snatched your hand off.
“So I think, on reflection, it has been a positive reaction.”