| 1. Round | 03/08/2024 | Partick Thistle | - | Greenock Morton FC | 0:0 | ||||
| 2. Round | 10/08/2024 | Greenock Morton FC | - | Hamilton Academical | 0:0 | ||||
| 3. Round | 24/08/2024 | Livingston FC | - | Greenock Morton FC | 1:1 | ||||
| 4. Round | 31/08/2024 | Greenock Morton FC | - | Falkirk FC | 2:3 | ||||
| 5. Round | 14/09/2024 | Queen's Park FC | - | Greenock Morton FC | 1:0 |  |
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| 6. Round | 21/09/2024 | Greenock Morton FC | - | Airdrieonians FC | 2:0 | ||||
| 9. Round | 19/10/2024 | Dunfermline Athletic | - | Greenock Morton FC | 0:0 | ||||
| 10. Round | 26/10/2024 | Hamilton Academical | - | Greenock Morton FC | 3:0 | ||||
| 13. Round | 08/11/2024 | Greenock Morton FC | - | Ayr United | 1:1 | ||||
| 14. Round | 16/11/2024 | Raith Rovers | - | Greenock Morton FC | 2:3 |
Scotland