Dundee started with one change from the Dumbarton game when Jon McCracken replacing Adam Legzdins in goal. New loan signing Amadou Bakayoko was on the bench, along with Luke McCowan.
Dundee started well and Diego Pineda had two good efforts on goal, but after that Inverness CT had a couple of breaks and forced Jon McCracken to tip one over the ball.
Dundee struggled for the rest of the half as they failed to create anything clear cut in the last third of the field. ICT were not much better as the half finished 0-0.
Second half and Dundee Manager Tony Docherty made changes at half time. Scott Tiffoney and Diego Pineda was substituted by Lyall Cameron and Amadou Bakayoko. The newcomers immediately injected more life and purpose into the Dee attacks.
Bakayoko was unlucky with a 18 yard shot as Dundee looked more dangerous going forward. Then Luke McCowan came on for Josh Mulligan as Dundee stepped up their attacks.
It paid off on 60 minutes Boateng combined with Bakayoko on the left. Cameron fed the first cross back to Boateng who crossed for McCowan. His shot was blocked by Duffy but Zach Robinson was on hand to head for goal. Ridgers clawed the ball out, but it was already a yard over the line.
Inverness CT had a few attacks but nothing on target to trouble Dundee, who now was going for the vital second goal. McCowan had a effort on goal which was saved and the rebound never fell kind to the Dundee forwards. Then Beck had a shot but it was too straight to the keeper.
McCowan went down in the box but the Referee waved play as Dundee gave it their all in a bid to score. Time ran out and Dundee would fail to go onto the next stage of the League Cup.
Hard way to go out they needed to score 1 more goal over the four games to go through.
Dundee: McCracken, Ashcroft, Shaughnessy, Portales, Mulligan (McCowan 57), McGhee (Robertson 76), Boateng, Beck, Tiffoney (Cameron at half time), Pineda (Bakayoko at half time), Robinson. Unused Subs: Legzdins (gk), Kerr, Rudden, Anderson, Wilkie.
Referee: John Beaton
Att: 2,337