Stephen Robinson rued an "opportunity missed" after his Motherwell side were knocked out of the Europa League in Israel by Hapoel Beer Sheva.
Despite going 1-0 down at half-time to Leonardo Vitor's header, the away side had plenty of the game before Declan Gallagher's second-half sending off.
He earned a second yellow after giving away a penalty which Josue converted, with Elton Acolatse sealing the game.
"We had so much of the game," said manager Robinson of the 3-0 defeat.
"After 30 minutes, we felt we had a right chance. We were so disciplined and organised, and we had chances. We certainly matched them for long periods."
Four wins from five games had infused the Lanarkshire side with confidence, and they started this third qualifying round tie well.
Motherwell moved the ball swiftly in the early stages while keeping a tight structure, until a defensive lapse from Ricki Lamie allowed Jhonatan Agudelo to lash a volley high and wide.
The Scottish Premiership side's first attempt was saved spectacularly as Ohad Levita got down low to deny Christopher Long's close range turn-and-hit, before Trevor Carson made an impressive save of his own, diverting Acolatse's effort past his near post.
However, the Northern Ireland goalkeeper could do nothing about the opener. Just minutes before the break, Josue delivered a dangerous free-kick from deep and captain Vitor powered in a header.
The goal was a sucker punch for Robinson's men, but they came out fighting in the second period as they squandered a glorious chance to level as Gallagher put a free header over the bar.
Similar to the first half, the Fir Park club began to take control, but they were unable to capitalise on another promising spell as a dangerous delivery from Josue resulted in Gallagher dragging Vitor to the deck, Josue converting calmly from the spot.
The game was effectively gone at that point, but Beer Sheva were not done as Acolatse wrapped up the scoring after finishing well down to Carson's left following a neat one-two with Sintayehu Sallallich.
Man of the match - Josue
What did we learn?
Motherwell were rightly regarded as underdogs, given they were facing a team who have featured in the Europa League group stages in two of the previous four seasons, but Robinson will view this as an opportunity missed. The Scots had spells throughout, but lacked a clinical edge.
What they said
Motherwell manager Stephen Robinson: "We done ever so well at times, but at that this level we concede from two set plays which is so disappointing.
"We were a little bit naive with things. I'm pleased with the young boys, but there are lots of lessons to be learned. There's a tinge of disappointment because it wasn't like we got played off the park."
Motherwell return to league duties this Sunday as they welcome Rangers to Fir Park (12:00 BST).
Hapoel Be'er Sheva
- 35BareiroBooked at 58mins
- 4Leonardo Vítor
- 30DadiaBooked at 54mins
- 20TahaBooked at 45mins
- 8KabhaBooked at 15mins
- 10Soares Pesqueira
- 7AcolatseSubstituted forYosefiat 86'minutes
- 32AgudeloBooked at 56minsSubstituted forVarenneat 59'minutes
- 16SallalichSubstituted forMeliat 86'minutes
- 31GallagherBooked at 70mins
- 99LongSubstituted forLangat 72'minutes
- 33O'DonnellBooked at 56mins
- 19PolworthSubstituted forMaguireat 86'minutes
- 32WattBooked at 45minsSubstituted forWhiteat 75'minutes
- Serhiy Boyko