| 1. Round | 12/09/2020 | Crystal Palace | - | Southampton FC | 1:0 |  |
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| 2. Round | 19/09/2020 | Manchester United | - | Crystal Palace | 1:3 | ||||
| 3. Round | 26/09/2020 | Crystal Palace | - | Everton FC | 1:2 | ||||
| 4. Round | 03/10/2020 | Chelsea FC | - | Crystal Palace | 4:0 | ||||
| 8. Round | 07/11/2020 | Crystal Palace | - | Leeds United | 4:1 | ||||
| 18. Round | 14/01/2021 | Arsenal FC | - | Crystal Palace | 0:0 | ||||
| 19. Round | 17/01/2021 | Manchester City | - | Crystal Palace | 4:0 | ||||
| 21. Round | 30/01/2021 | Crystal Palace | - | Wolverhampton Wanderers | 1:0 | ||||
| 25. Round | 22/02/2021 | Brighton & Hove Albion | - | Crystal Palace | 1:2 | ||||
| 26. Round | 28/02/2021 | Crystal Palace | - | Fulham FC | 0:0 | ||||
| 29. Round | 03/03/2021 | Crystal Palace | - | Manchester United | 0:0 | ||||
| 31. Round | 10/04/2021 | Crystal Palace | - | Chelsea FC | 1:4 | ||||
| 33. Round | 26/04/2021 | Leicester City | - | Crystal Palace | 2:1 | ||||
| 36. Round | 16/05/2021 | Crystal Palace | - | Aston Villa | 3:2 | ||||
| 37. Round | 19/05/2021 | Crystal Palace | - | Arsenal FC | 1:3 | ||||
| 38. Round | 23/05/2021 | Liverpool FC | - | Crystal Palace | 2:0 |
Scotland
