Trailing 5-1 from the first leg, a result that came to look even more ridiculous as the Romanians wilted under pressure and lashed out in the closing stages, David Moyes' team rallied superbly in an opening 45-minute spell that suggested they would go close to matching Liverpool's extraordinary Champions' League final comeback.
Real Madrid were the last team to overturn such a first-leg deficit and Everton did not possess the pedigree or predatory prowess to turn their most vibrant attacking display of the season into a four-goal margin such as enabled the Spaniards to overcome Borussia Mönchengladbach in the same competition 20 seasons ago.
They can still draw consolation from a display that belied their Premiership position, but the unpalatable truth for Moyes is that the endeavours of last season, when they defied the odds to finish fourth, have amounted to little more than a fall at the first hurdle of two European competitions and a hangover that has impacted on their League campaign.
It was far more painful for Arteta, the stylish Spanish midfielder, who spent the night under observation in a Merseyside hospital following an appalling challenge by Mihaita Plesan. The Bucharest midfielder led with his arm as he leapt into the back of Arteta's head, sending the 23-year-old into convulsions on the pitch and resulting in his departure on a stretcher and in a neck brace. Combined with several spitting incidents by the Romanians, it was a fraught end to an unhappy European experience for Everton.
"Fortunately Mikel is fine at the moment," said Moyes. "We think it is a neck injury and they will keep him in overnight but it was a horrible challenge and I am sure if Duncan [Ferguson] had done that he would have been sent off."
Plesan was only booked for his assault, as the French referee Laurent Duhamel struggled to keep control. "To be fair they probably thought we were rough and ready too," admitted Moyes.
The final scoreline failed to reflect a vibrant start by Everton that should have yielded more than the 28th-minute header from Tim Cahill when he sent a trademark header, albeit his first of this season, beyond Uladzimir Hayeu following a fine combination between Arteta and Ferguson.
The supply line to the Scot was accurate and regular, with his strike partner James McFadden going close several times in the opening half-hour, but ultimately Dynamo wised up to the home team's tactics.
"The plan was to get a second goal in the first half to give us something to go at in the second and I thought we should have got that," Moyes said. "We gave it a good go, though, we really did. It was a night when we couldn't afford to miss many opportunities but we did. We should never have been 5-1 down from the first leg, we know that, but it was a terrific effort from the players."
Everton (4-4-2): Martyn; Hibbert (Weir, 24), Yobo, Ferrari, Valente (Bent, 68); Arteta, Neville, Cahill, Kilbane (Beattie, 68); Ferguson, McFadden. Substitutes not used: Wright, Li Tie, Osman, Wilson.
Dynamo Bucharest (4-4-2): Hayeu; Galamaz, Tamas, Moti, Pulhac; Petre, Margaritescu, Grigorie, Plesan; Bratu (Chihaia, 83), Zicu (Baltoi, 74). Substitutes not used: Daouda, Goian, Cristea, Munteanu, Matache.
Referee: L Duhamel (France).Reuse content