Falkirk fell to a 1-0 defeat against St Johnstone at McDairmid Park on Tuesday evening.
A first half goal from Stefan Scougall was enough for the hosts to secure the three points and go top of Group B.
Falkirk started the game brightly. Deimantas Petravicius was a target for Saints defenders from the off, and was taken out by Liam Craig and Murray Davidson.
The Lithuanian took exception to one tackle from Craig, pushing the midfielder down - but nobody was for getting involved.
It was Petravicius who created Falkirk's best chance of the first half. His corner was delivered well but hooked clear by Steven Anderson.
St Johnstone took the lead on the half hour mark through Stefan Scougall. A neat reverse pass from Richard Foster set the striker free and he side-footed past the helpless Leo Fasan for 1-0.
The hosts dominated the ball well after taking the lead, not allowing Falkirk to create.
Murray Davidson's acrobatic effort was the last chance of the first period for either side, but was easily saved by Fasan.
Into the second period and the Bairns looked the better side for the opening stages.
Aaron Muirhead's ball found Tom Owen-Evans, but his shot was blocked.
St Johnstone had a big chance on the hour mark, but Liam Gordon was denied by Fasan and Murray Davidson's follow up was blocked.
Both sides struggled to create anything after the hour, with St Johnstone having slightly the better openings. Kyle McClean dragged wide after 70 minutes - which was the best chance until the end of the game.
Tommy Wright's Saints should have sealed the victory in the 90th minute. David McMillan's effort was cleared off the line before Davidson's effort was blocked out for a corner.
The last chance of the game, though, was to go Falkirk. And it was their best chance of the match.
Having won a corner from nowhere, Scott Harrison controlled the ball brilliantly in the area, took a touch and fired a low shot which was saved by Zander Clark to the sound of the full time whistle.
Falkirk are not officially out of the tournament, but need more than a miracle to have a hope of qualifying for the next round.