David Moyes insists West Ham still have “half a chance” to reach the Europa League semi-finals despite an agonising 2-0 first-leg defeat at Bayer Leverkusen.

The Hammers defended heroically for 83 minutes of a one-sided encounter against the Bundesliga leaders in Germany.

But late goals from substitutes Jonas Hoffman and Victor Boniface left West Ham with it all to do in next week’s second leg against a team yet to lose a match this season.

Moyes told TNT Sports: “Leverkusen have a good record of scoring late. We were aware of that. We did a great job but we played against a Champions League side and we’re not quite at that level.

“We’re still in the tie and we have half a chance in the second leg.

“We’d like to have played more attacking. The players did a brilliant job with the structure. We got done by two corner kicks. The second one was really poor from our point of view.

“It’s going to take some performance because they’re a really good team. You never know what’s going to happen. Let’s try to get one and then see if we can get two. We’ll pick ourselves up for next week and hopefully get the crowd behind us.

“This team we’re playing will be Champions League next year. We have to recognise what we’re playing against. We’ll have to do exceptionally well to get that result.”

Goalkeeper Lukasz Fabianksi made a string of excellent saves to keep the hosts at bay.

The former Poland international, who turns 39 next Thursday, added: “We are very disappointed.

“We worked hard for 80 minutes and then we gave two goals away from set-pieces. Usually defending set-pieces is our strength but you have to give a lot of credit to the opposition because they pushed the whole game.

“The more disappointing thing is that we conceded the second goal. It gives them a bit more confidence. We won’t give up. We have to believe and respond in the second leg.

“I wouldn’t say we ran out of energy. Both teams did their best. In the end the second set-piece felt too easy. It felt like the striker had too much space.

“We have a really good record at home. They’re special magical nights and hopefully the second leg will be the same.”

To make matters worse, West Ham will be without Lucas Paqueta through suspension for the return leg.

Leverkusen’s former Arsenal midfielder Granit Xhaka said: “We knew before the game West Ham would be deep, but we showed one more time we have the quality to beat these teams.

“The second goal helps a lot for the second leg and we’ll have to be focused from the beginning.”

West Ham were breached by two late goals as they slipped to a 2-0 defeat in the first leg of their Europa League quarter-final at Bayer Leverkusen.

The Hammers had defended heroically for 83 minutes before goalkeeper Lukasz Fabianski was finally beaten by substitute Jonas Hoffman.

A one-goal deficit might have given David Moyes’ side hope going into next week’s second leg at the London Stadium, despite facing a side unbeaten all season.

But disaster struck in stoppage time when a second substitute, Victor Boniface, headed home Hofmann’s cross, to leave West Ham’s hopes of a third consecutive European semi-final looking horribly slim.

A yellow card for Lucas Paqueta, ruling the Brazil international out of the second leg, only adds to the task facing the east Londoners.

The Hammers, without injured top scorer Jarrod Bowen and defensive midfield linchpin Edson Alvarez through suspension, were almost undone in the seventh minute when Josip Stanisic’s wayward shot was flicked towards goal by Patrik Schick but the ball went straight to Fabianski.

But Leverkusen were given a warning of West Ham’s prowess on the counter-attack moments later when Michail Antonio outstripped Jonathan Tah on the left wing and produced the best chance of the first half.

The burly frontman squared the ball to Mohammed Kudus, but the Ghana winger’s first-time strike was comfortably held by Matej Kovar.

However, West Ham were largely camped in their own penalty area and Fabianski palmed away Jeremie Frimpong’s curler before Exequiel Palacios’s drive was deflected over.

Paqueta’s over-enthusiastic challenge on Amine Adli earned him his booking – the Brazilian survived a red card check – and provoked a mild skirmish on the touchline.

Fabianski might have suspected he was in for a busy evening and he was proved right, making big saves to keep out dangerous efforts from Alejandro Grimaldo, Shick and Edmond Tapsoba.

Early in the second half Emerson Palmieri was shown a yellow card after catching Adli on the ankle, meaning the left-back will also sit out next week’s return leg.

Frimpong, a former Manchester City youngster, hit a low angled drive straight at Fabianski, before the 38-year-old Pole made a stunning save to tip Shick’s instinctive header over the crossbar.

But with seven minutes remaining Fabianski was powerless to prevent Hoffman’s shot bouncing through a sea of white shirts and into the net after a corner was only half-cleared.

Tomas Soucek cleared two Tah efforts off the line in a desperate finale before Boniface headed the second to leave the Hammers devastated.