Just nine years on from being a non-league side, the newly-promoted Hatters were taught a punishing lesson on their first return to top-flight action since relegation from the old First Division in 1992.
Carlton Morris’ 81st-minute penalty gave Town hope of snatching something at the Amex Stadium after Joao Pedro’s spot-kick added to Solly March’s first-half header.
But, despite some encouraging signs, they were second best on the south coast and ultimately suffered a resounding loss following late finishes from Seagulls substitutes Simon Adingra and Evan Ferguson.
“We have to do it our way,” said manager Edwards. “We have got a plan, we’ve had that over the last decade or so and had a lot of success.
“We’re now going into what’s probably going to be the biggest challenge the club’s had. We know the scale of the challenge. We’re going to have some tough days.
“I don’t want anyone to be happy about losing football matches – we’re certainly not.
“I was pleased with stuff I saw today. I know we’re going to get better. But we’ve got to get better quickly.”
March nodded the hosts ahead nine minutes before the break before Brighton’s £30million record signing Pedro slotted home from 12 yards, having been brought down by Luton captain Tom Lockyer.
Morris’ successful spot-kick, after Jacob Brown’s cross struck the elbow of Lewis Dunk, looked to have set up a tense finale.
But an inexplicable error from Pelly Ruddock Mpanzu allowed Albion debutant Adingra to swiftly restore the hosts’ two-goal advantage before fellow substitute Ferguson added another deep into stoppage time.
Edwards, who felt both penalty decisions were “harsh”, was left to rue his side’s mistakes.
“I thought we were right in the game at 1-0 and at 2-1 but we shot ourselves in the foot,” he said.
“We made a couple of clear errors in the build up to the third goal and we got punished and at this level you do get punished.
“It shows the ruthless nature of the league.”
Brighton set aside Moises Caicedo’s ongoing transfer saga to launch their first campaign to feature European football in commanding fashion.
Build up to the contest was dominated by news of Albion accepting a British record transfer fee of around £111million from Liverpool for the absent Ecuador midfielder amid reports he would prefer to join Chelsea.
Seagulls boss Roberto De Zerbi, who handed debuts to James Milner and Mahmoud Dahoud, in addition to goalscorers Pedro and Adingra, also lost Alexis Mac Allister to Liverpool during the summer, while Levi Colwill returned to parent club Chelsea.
The Italian warned it will take his team time to hit the heights of last season, which brought a club-record sixth-placed finish, and does not view Dahoud as a direct replacement for Caicedo.
“Dahoud is a great player for us because he’s specific for our idea of football, for our style of play,” he said.
“But we lost different characteristics because Dahoud is different from Moises Caicedo.
“We played well, not one of the best games in my time, but we need much time to reach the same level, the same quality of play of last season.
“We won a very tough game. I’m really pleased.”