Paul Hartley's Dark Blues ran up a 7-0 victory over Forfar but it was not enough to see them through to the last 16 as they ended up third in Group A.
Killie were held to a goalless draw by Albion Rovers at Rugby Park but Josh Magennis' spot-kick miss cost them dear in the shoot-out as their League Two opponents claimed a 5-3 triumph
Lee Clark's men did finish second in Group H but do not join the four best-placed runners-up moving into the next round.
However, group winners Peterhead, St Johnstone, Alloa, Partick Thistle, Rangers, Hamilton and Morton do progress to join Scotland's European entrants Celtic, Aberdeen, Hearts and Hibernian in the knockout stages.
Inverness will also top Group C so long as Dundee United do not better the 7-0 result Caley Thistle managed against Arbroath when they host Dunfermline on Sunday.
But Ray McKinnon's Terrors could also miss out completely if the Pars emerge victorious from Tannadice to join the other best-placed runners-up Motherwell, Queen of the South and Ayr United in the second round.
League One Peterhead were the surprise winners in Group A as they fought back to claims a bonus-point triumph at Dumbarton.
Kevin Dzierzawski put the Sons ahead only for Kevin Thomson to level Jim McInally's men level soon after.
David Smith's header and a Ryan Stevenson penalty re-established Dumbarton's lead but Leighton McIntosh's strike and a Rory McAllister penalty sent the game to penalties, with the Blue Toon triumphing 6-5.
Falkirk grabbed just their second win of the tournament thanks to second-half goals from former Rangers youngster Luca Gasparotto and striker Nathan Austin but it was not enough to see them escape Group B.
Greig Spence grabbed the only goal of the game at Stark's Park as Alloa beat Raith Rovers 1-0 to top Group D with a 100 per cent record.
In Group E, Queen of the South got a touch of fortune to claim second spot with a 1-0 win over Stenhousemuir when Jamie Hamill's cross-cum-shot found it's way past Warriors goalkeeper Colin McCabe with 12 minutes left.
Ryan Finnie's 25-yard piledriver and a late Max Wright spot-kick handed Annan their first Group F win as Lowland League minnows East Stirlingshire were beaten 2-0.
And St Mirren's failure to add to the three first-half goals they managed against Edinburgh City cost Alex Rae's side the chance to qualify from Group G.
The Buddies needed just one more goal to move above Ayr into second place but could only muster efforts from Lawrence Shankland, on-loan Rangers winger Tom Walsh and Jack Baird before the break.
Meanwhile, Morton avoided a slip-up to make sure of their place at the top of Group H as they overcame Berwick at Cappielow.
On-loan Celtic midfielder Jamie Lindsay slotted home four minutes into his debut before Jai Quitongo rounded Wee Rangers goalkeeper Kevin Walker to make sure of the win.
Source : PA
Source: PA