Everton slump to an embarrassing 5-2 defeat and exit the Europa League.
Dynamo Kyiv overturned their 2-1 first-leg deficit to move into the quarter-finals of the competition 6-4 on aggregate.
The outlook of the tie was transformed in the first half when Everton conceded on three occasions.
Andriy Yarmolenko opened the scoring with an arrowing shot from distance, before the Blues replied with an equally as impressive strike from Romelu Lukaku.
Lukasz Teodorczyk and Miguel Veloso then netted in quick succession to leave Everton facing an uphill battle and the task was put out of reach when Oleh Gusev converted from close-range and Antunes fired in a 30-yard thunderbolt in the second half.
Phil Jagielka scored with a flicked header eight minutes before the end but it was too little too late for the Blues.
Everton went into the game having made four changes to the team that started against Newcastle United the previous weekend. In came Christian Atsu, Gareth Barry, Steven Naismith and Ross Barkley, with Leon Osman, Arouna Kone, Darron Gibson and the ineligible Aaron Lennon making way.
The Olympic Stadium – venue of the Euro 2012 final – was at near full capacity and the locals were in loud voice from the outset, making for an intense atmosphere.
Oleh Gusev put Dynamo ahead early in the first meeting at Goodison – and he had two headed opportunities in the opening minutes.
The Blues dealt reasonably well with the poor pitch and the hosts’ early pressure – but Tim Howard was powerless to prevent the Ukrainian side from taking a 1-0 lead on the night after 20 minutes.
Yarmolenko picked the ball up 35 yards from goal, cut inside and found the top corner with an unstoppable left-foot shot from just outside the penalty area.
Everton’s response was encouraging and moments later Barkley was unlucky to see an effort from an acute angle strike the post and rebound to safety.
In an end-to-end first period, a fine Tim Howard save stopped Yarmolenko from scoring a second – before the Blues were back on level terms on the evening thanks to a stunning strike from Romelu Lukaku half an hour into the contest.
In similar fashion to the game’s opener, the Belgian found the target with a precise curling drive from distance, silencing the stadium apart from the 900-strong travelling Evertonians.
But back came Dynamo, with the home side striking twice in the space of four minutes to turn the tie on its head once again.
Teodorczyk pounced on some loose defending the area to make it 2-1 and not long after Everton were further behind when Portugal international Veloso volleyed into the roof of the net from 10 yards out.
With the prospect of extra-time and penalties no longer possible, Everton knew that if they were to reduce the deficit in the game to just one then they would progress on away goals.
But the Toffees’ hopes were dealt a hammer blow 10 minutes after the restart when Kyiv went further ahead on the evening and in the tie.
Yarmolenko was allowed space on the right-hand side of the Everton box and his cut-back was finished by Gusev, whose shot went into the net off the post.
Roberto Martinez’s charges tried to respond. Atsu forced Kyiv keeper Olexandr Shovkovskiy into a fine full-stretch save and Barkley hit the upright for a second time in the game, this time from long-range.
Kone and Osman were introduced with half an hour remaining but Everton were chasing the tie and that allowed Kyiv further goalscoring opportunities.
Substitute Denys Garmash drew a save out of Howard before Antunes left the Blues with a mountain to climb when he found the top corner from 30 yards out with a quarter of an hour remaining.
Yarmolenko hit the bar late on and there was still time for Jagielka to pull a goal back with a glancing header from a corner.
Everton pressed to the very end but ultimately it was an evening of disappointment as the Club’s continental quest came to its conclusion after 10 matches in the competition.