Matches: 1971 – 1972 | Match Pictures: 1971-72 | League Cup |
Celtic were in Group 4
| Ayr Utd |
1 – 1 | Morton |
|
| Celtic |
2 – 0 |
Rangers |
Link |
| Morton |
0 – 1 |
Celtic |
Link |
| Rangers |
4 – 0 |
Ayr Utd |
|
| Ayr Utd |
0 – 3 |
Celtic |
Link |
| Rangers |
2- 0 |
Morton |
|
| Ayr Utd |
0 – 4 |
Rangers | |
| Celtic |
0 – 1 |
Morton |
Link |
| Morton |
2 – 0 |
Ayr Utd |
|
| Rangers |
0 – 3 |
Celtic |
Link |
| Celtic |
4 – 1 |
Ayr Utd |
Link |
| Morton |
0 – 1 |
Celtic |
Final Group table
| Team | P | W | D | L | F | A | GD | Pts |
| Celtic | 6 | 5 | 0 | 1 | 13 | 2 | +11 | 10 |
| Rangers | 6 | 4 | 0 | 2 | 11 | 5 | +6 | 8 |
| Morton | 6 | 2 | 1 | 3 | 4 | 5 | -1 | 5 |
| Ayr Utd | 6 | 0 | 1 | 5 | 2 | 18 | -16 | 1 |
Celtic were joined by the following teams in the Quarter Finals
| Group | Team | W | D | L | F | A | GD | Pts |
| 1 | Hibernian | 5 | 1 | 0 | 14 | 3 | +11 | 11 |
| 2 | Falkirk | 4 | 1 | 1 | 12 | 6 | +6 | 9 |
| 3 | St Johnstone | 3 | 1 | 2 | 8 | 7 | +1 | 7 |
| 4 | Celtic | 5 | 0 | 1 | 13 | 2 | +11 | 10 |
| 5 | Clydebank | 4 | 2 | 0 | 17 | 9 | +8 | 10 |
| 6 | Stirling Albion | 5 | 1 | 0 | 14 | 7 | +7 | 11 |
| 7 | Partick Thistle | 4 | 2 | 0 | 18 | 6 | +12 | 10 |
| 8 | St Mirren | 4 | 0 | 2 | 10 | 5 | +5 | 8 |
| 9 | Alloa | 1 | 3 | 0 | 5 | 2 | +3 | 5 |
Alloa qualified from the expanded Group 9 of 5 teams
Supplementary Round:
Partick Thistle 4 – 1 Alloa
Alloa 1 – 1 Partick Thistle
Aggregate:
Partick Thistle 5 – 2 Alloa
Quarter Finals
| Team | Agg. | Team | 1st Leg | 2nd Leg | Playoff |
| Clydebank |
2-11 | Celtic |
0-5 | 2-6 | |
| Falkirk |
2-1 | Hibernian |
2-0 | 0-1 | |
| St Johnstone |
3-5 | Partick Thistle |
2-0 | 1-5 | |
| St Mirren |
5-0 | Stirling Albion |
2-0 | 3-0 |
Semi Finals:
| Team | Team | |
| Partick Thistle |
2-0 | Falkirk |
| Celtic | 3-0 | St Mirren |
Final:
Played at Hampden Park, 23rd October, 1971.
Partick Thistle 4 – 1 Celtic
Winners League Cup 1971-72 Partick Thistle