England's last remaining team exited European competition as Everton were soundly beaten in their last-16 Europa League tie against Dynamo Kiev.
In a week where Manchester City and Arsenal exited the Champions League, poor defending cost Everton in Ukraine, as they lost 6-4 on aggregate.
Romelu Lukaku's strike cancelled out Andriy Yarmolenko's wonderful opener.
But Lukasz Teodorczyk, Miguel Veloso, Oleg Gusev and Antunes scored, before Phil Jagielka's headed consolation.
Everton's resounding 5-2 defeat in Kiev ends a dismal month for English sides in Europe, with Chelsea, Liverpool and Tottenham also knocked out.
The collective failings mean the country does not have a side in the last eight of the Europa League or Champions League for the first time since 1995.
It will pose further questions on the strength of the domestic game and Martinez will likely be quizzed about his team's defensive generosity as they surrendered a 2-1 first-leg lead in their first European away loss of the season.
Though they can look at two Ross Barkley efforts which hit the post as unfortunate, indecision littered their work at the back as hopes of a first European trophy since 1985 were ended.
Here's how the game unfolded:
Dynamo Kiev 1-0 Everton (2-2 agg) - Andriy Yarmolenko (21 mins)
Individual brilliance: Andriy Yarmolenko opened the scoring. He has been involved in 10 Europa League goals this season
Andriy Yarmolenko picked up the ball halfway inside Everton's half and cut in from the right, administering a double step-over before shooting left footed from 25 yards into the top corner, leaving Tim Howard motionless.
It was a goal of superb quality, but Ukraine's Player of the Year - an award won six times by Andriy Shevchenko - was allowed time to run from the right flank, create space and fire the home side level in the tie but ahead on away goals.
Dynamo Kiev 1-1 Everton (2-3 agg) - Romelu Lukaku (29 mins)
Rom's stunner: Romelu Lukaku scored his eighth goal of the Europa League campaign to level on the night
Everton trained on the running track surrounding the pitch on Wednesday, such was the concern over the pitch at the Olympic Stadium, but the surface did little to prevent high quality finishing.
After Barkley had struck the post and Tim Howard denied Yarmolenko a second, Lukaku curl a wonderful left-foot effort around a defender and in from 20 yards. The 21-year-old is the tournament's joint top scorer with FC Salzburg striker Alan on eight goals.
Dynamo Kiev 2-1 Everton (3-3 agg) - Lukasz Teodorczyk (35 mins)
Calamity at the back: Lukasz Teodorczyk gave Dynamo the lead on the night from six yards, prodding through Tim Howard's legs
The first of two quick-fire home goals from long diagonal balls arrived when Teodorczyk prodded through Howard's legs from six yards from Yarmolenko's knock-down.
It took Yarmolenko's haul of assists in the competition to seven, a tournament high, but underlined the indecision and apprehensive defending that was to follow as Jagielka, and particularly Antolin Alcaraz, struggled.
Dynamo Kiev 3-1 Everton (4-3 agg) - Miguel Veloso (37 mins)
Alcaraz punished: Antolin Alcaraz's poor header clear is lashed back with interest by Miguel Veloso
Another long diagonal, this time from right to left, saw midfielder Miguel Veloso win a flick-on. When Alcaraz could only head to the edge of his area, Veloso volleyed left-footed high into the net, with a deflection leaving Howard helpless.
The goal ended any chance of extra time but a single goal would have carried Everton through to a first European quarter-final in 30 years on away goals. But with Alcaraz increasingly under pressure at every turn, the prospect of preventing further damage looked unlikely.
Dynamo Kiev 4-1 Everton (5-3 agg) - Oleg Gusev (56 mins)
Ponderous Blues: Oleg Gusev scores his second of the tie, cracking in off the post from six yards
The man who started the scoring in the first leg was in the right place at the right time as he stabbed in at the second attempt from six yards. Again, the visitors were sliced open and were found wanting when the pull-back to Gusev arrived.
Sergiy Rebrov's side have been superb at the Olympic Stadium this season and have now won by at least a two-goal margin in all of their Europa League home games.
Dynamo Kiev 5-1 Everton (6-3 agg) - Antunes (76 mins)
Antunes missile: Defender Antunes finished like a seasoned striker from 30 yards
Everton winger Christian Atsu forced a diving save from 40-year-old Oleksandr Shovkovskyi and Barkley whipped a dipping, curling effort onto the post as the Premier League side battled. But Antunes, a player signed from Malaga this year, took aim from 30 yards with a left-foot strike which again left Howard with no chance as it found the top corner.
Everton could be heavily criticised for three of the five goals they conceded but those from Yarmolenko and Antunes were individually brilliant.
Dynamo Kiev 5-2 Everton (6-4 agg) - Phil Jagielka (82 mins)
Exit point: Though Phil Jagielka headed a consolation, Everton's players were well beaten on a tough night
Remarkably, after Yarmolenko had hit the bar from inside the area, Phil Jagielka's near-post header gave Everton some hope.
Though Baines had a free-kick blocked and Lukaku forced two saves, more goals would not arrive and the visitors are now left with only a scrap against relegation to fill the remainder of their season and the prospect of no European football in 2015-16.
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