Shels had a two-goal advantage after the first leg finished 3-1 at Tolka Park and they never looked like folding.
First half strikes from Harry Wood and Ali Coote ensured the Dublin side were cruising 2-0 ahead on the night and 5-1 on aggregate.
That’s how the tie finished as a sensational Linfield fightback never materialised.
“That was disappointing,” said Healy. “We wanted to score the first goal and never gave ourselves that chance. It was a disappointing level of performance.
“All credit to Joey (O’Brien) and his team who fully deserved their victory, and we wish them well.
“That was our most disappointing performance against Shelbourne in the most important of the four games. That is frustrating for me as manager.
“Shelbourne managed the game well, they scored their goals and were better than us from one to 11, collectively and individually – it was as simple as that.”
Since dropping into the Conference League, Linfield saw off Zalgiris of Lithuania and Vikingur of the Faroe Islands but Shelbourne were a different animal.
Two goals in a devastating seven-minute spell in the first half ensured this was a stroll for Shels.
David Healy
News Catch Up – Friday 29th August
It was a memorable night for the League of Ireland with Shamrock Rovers also progressing to the League phase.
“It wasn’t a case of the occasion affecting players,” said Healy.
“I wouldn’t think that way. If we couldn’t play a game like this I wouldn’t go out of my way to sign players.
“They are disappointed and we have to move on. There is a big difference between the leagues.
“Shelbourne lost their manager (Damien Duff) in mid-season but it has been a seamless transition with Joey.”
The Shelbourne team and supporters celebrate after the game
This result is Linfield’s third Play-Off defeat in six years.
Healy’s side had twice been on the cusp of reaching a major competition – they were knocked out on away goals by Qarabag in a Europa League Play-Off in 2019 and came within seconds of qualifying for the Conference League three years later before ultimately losing out on penalties to RFS.
Shels boss O’Brien said: “We have learned so much from these games and can now look forward to more.
“It’s about the players and fans for me. It is a great night for Irish football. I believed in the players, otherwise I wouldn’t have taken the job.
“It’s a wonderful achievement by the club and it’s important they embrace it.
“Our League has grown and we needed to take advantage of the champions path.
“With Ollie Horgan (former League of Ireland manager) passing away, our achievements are a nice tribute to him.”