Everton’s misery deepened as they crashed out of the Europa League with two Group E games left to play following a heavy defeat in Lyon.

The former Chelsea forward Bertrand Traoré, who scored the winner in Lyon’s 2-1 victory at Goodison Park a fortnight ago, opened the scoring midway through the second half, before the substitute Houssem Aouar and the former Manchester United man and Everton transfer target Memphis Depay wrapped things up.

The 80th-minute dismissal of Morgan Schneiderlin, following a second yellow card, capped another awful night for Everton, who also had Cuco Martina taken to hospital after the full-back fell awkwardly. Martina was able to fly back from France with his team-mates on Thursday evening after undergoing scans, no little relief given the distressing scenes when, after several minutes’ treatment on the pitch following a heavy fall, the Dutchman was carried from the field wearing a neck brace.

The right-back had landed awkwardly following an aerial challenge with Maxwel Cornet after 43 minutes. Amid fears of Martina having sustained serious damage, Everton sent out a message on their official Twitter feed which said he would be kept in hospital overnight for observation. But it subsequently emerged that following scans, the 28-year-old had been cleared to travel back to Merseyside with the squad.

Everton’s Cuco Martina is carried off injured after a terrible fall in the first half. Photograph: Laurent Cipriani/AP

The defeat, Everton’s fifth in a row in all competitions, combined with Atalanta’s 1-1 draw at Apollon Limassol, means the bottom-placed side cannot reach the last 32. Three of the defeats have come since Ronald Koeman’s sacking, and while the caretaker manager, David Unsworth, has made it clear he would like the role full-time, the results so far are not strengthening his position.

Unsworth said of his job prospects: “It’s not about me, it’s about the football club and what will be will be, I’ve said all along. Whoever gets the honour of being Everton manager, other people will decide that. It’s about getting over this disappointing result and taking the positives and picking a team to win a massive game on Sunday [against Watford at Goodison].

“It’s a cup final for me. I’ll be doing everything I can to make sure everybody is prepared. I’ll pick a team to win against a decent Watford team. Sunday is a huge game for me, huge game for the club and I’ve left the players in no uncertain terms it’s a huge one for them as well. I’m sure they will respond and I’m sure the Goodison faithful will get behind us all … we need three points on Sunday.”

Unsworth opted to rest the experienced trio of Wayne Rooney, Leighton Baines and Phil Jagielka for this contest, and his starting line-up – featuring six changes – had no recognised striker, with Gylfi Sigurdsson starting as a “false nine”.

The caretaker manager had spoken about Everton “giving it everything to win” in a competition that was important to them – but the selection only emphasised the significance of Sunday.

After the hosts exerted some early pressure, with Mouctar Diakhaby just failing to convert Depay’s free-kick at the back post, Everton settled and a tidy passing move led to the ball falling to Sigurdsson in the Lyon box in the 18th minute – but he could not produce a decent shot.

Lyon were soon back on the front foot and Jordan Pickford made a fine double save, parrying Traoré’s header and blocking a follow-up effort from Nabil Fekir, who then sent a shot over the bar.

Sigurdsson was beaten by his marker to a good cross from Jonjoe Kenny, and Mason Holgate was then fortunate not to score an own goal as he diverted a Maxwel Cornet cross into Pickford’s arms.

Pickford pushed away a Depay free-kick, before the game was halted for several minutes as Martina received treatment having fallen awkwardly after an aerial challenge with Cornet.

Replays indicated Martina may have been knocked out, and he was eventually carried off the field on a stretcher, with Muhamed Besic coming on to operate at right-back.

In the seven minutes of added time that followed before the interval Pickford made another stop, keeping out a shot from Traoré. An excellent chance came Everton’s way early in the second half when Ademola Lookman teed up Idrissa Gueye, who saw his strike saved by Anthony Lopes and probably should have done better.

After Lyon appeals for a penalty when Fekir went down under the attentions of Holgate were waved away by the referee, Lookman sent a cross to the near post where Sigurdsson tried to meet it but barely made contact.

It looked as if Everton might be building some momentum, but the game then got away from them entirely. First Traoré collected the ball, burst forward and slotted past Pickford in the 68th minute, then eight minutes later Pickford blocked a Mariano Diaz effort but was beaten by a shot from Aouar, who was set up by Depay. And after Schneiderlin was dismissed, Depay completed the scoring with a header two minutes from time.

Memphis Depay celebrates scoring the third goal against Everton. Photograph: Jean Catuffe/Getty Images

Unsworth said: “I’m really disappointed, for nearly 70 minutes we were nearly perfect with our gameplan and created a couple of opportunities we could and should have scored. The first goal was a lucky ricochet which gets the lad in. The second goal was a killer, long ball down the middle of the park and we don’t deal with it.

“The effort was there, the commitment was there. We showed some nice touches and created a couple of opportunities against a very god Lyon team. We just can’t cave in when we concede a goal. That’s something we need to rectify very, very quickly going into Sunday’s game.”