Arsenal took a sixth-minute lead through Kai Havertz and spent much of the match at the Puskás Aréna in Budapest defending that advantage, deploying a deeply conservative approach designed to hold their lead and take the game to penalties if necessary.
Paris Saint-Germain eventually forced the game into extra time and won 4-3 on spot-kicks, with Gabriel Magalhães blazing the decisive penalty over the bar.
Speaking on RMC Sport's Rothen s'enflamme programme, Dugarry was withering.
"Arsenal is and will remain the greatest club never to have won the Champions League. Congratulations, what a source of pride. They did absolutely nothing. At no moment did they come onto the pitch to create anything. We saw long balls hoofed into the air. We saw a team that systematically wasted time. It was unbearable, insufferable."
He went further, suggesting the manner of Arsenal's approach had nearly constituted a scandal for the sport.
"What almost would have been terrible for football is that they almost gave the illusion that by doing so little, you can win the Champions League. They are frauds.
"I am so happy that it blew up in their faces. If they ever want to win it, they need to start playing football. That is not Arsenal. There is a history in this club. They cannot play like that. If they had won it, it would have been a scandal."
Jamie Carragher, the former Liverpool defender, offered a similarly sharp assessment on a separate broadcast, saying Arsenal had appeared to be "trying not to lose" rather than win, and called it one of the worst performances ever seen in a final.
Mikel Arteta signalled after the match that significant recruitment is coming, indicating the club's ambition to close the gap that the defeat exposed. Whether that gap is one of personnel or approach remains the central question heading into the summer.