Arsene Wenger had admitted his players were less than keen to make this journey and that much was plain to see last night. Outfought and outplayed, this was a spineless, if meaningless, end to Arsenal's Group B campaign.
They go into Friday's second-phase draw in any event and, to the delight of the locals, Shakhtar Donetsk will continue their European adventure in the UEFA Cup.
Shakhtar began positively and enjoyed the majority of possession, though without initially threatening to break an Arsenal defence which featured Matthew Upson at its centre and Stuart Taylor making only his second first-team appearance in goal.
It was no great surprise, therefore, when they made the breakthrough in the 35th minute. Anatoliy Tymoshchuk's long ball caught out Martin Keown and left Sergei Atelkin bearing down on goal to finish via the post.
Arsenal fell further behind when Vivas conceded a free-kick just outside his penalty area in the 57th minute and Andriy Vorobei curled his shot over the wall and into the right corner.
Having scored that one, Vorobei set up the third, crossing from the right for the substitute to Olexiy Bielik to volley in as Keown failed to intercept. For Arsenal the flight home could not come fast enough.
SHAKHTAR DONETSK (4-4-2): Virt; Starostyak, Okoronkwo, Popov, Gleveckas; Zubov, Tymoshchuk, Bakharev, Abramov (Aliuta, 78); Atelkin (Bielik, 52min), Vorobei (Savu, 86).
ARSENAL (4-4-2): Taylor; Dixon, Keown, Upson, Cole; Parlour (Vernazza, 72), Kanu, Vivas, Lauren; Wiltord, Henry (Ljungberg, 62) .
Referee: K Fisker (Denmark).