Gary Hooper's winner 10 minutes from time has seen the Bhoys leapfrog Motherwell and leave them 12 points behind rivals Rangers with a game in hand.
"If you want to go and win the title then I think the game was a must-win," said Thompson.
"If we don't win today it is virtually impossible but we hung on in there."
Celtic next host Inverness in the SPL after the international break.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| Championship Group | |||||||||
| 1 | Celtic | 0 | 0 | 0 | 0 | 80 | 26 | 54 | 78 |
| 2 | RangersRangers | 0 | 0 | 0 | 0 | 72 | 23 | 49 | 75 |
| 3 | Hearts | 0 | 0 | 0 | 0 | 46 | 34 | 12 | 62 |
| 4 | Kilmarnock | 0 | 0 | 0 | 0 | 43 | 34 | 9 | 51 |
| 5 | St Mirren | 0 | 0 | 0 | 0 | 38 | 43 | -5 | 43 |
| 6 | Dundee | 0 | 0 | 0 | 0 | 44 | 54 | -10 | 41 |
| Relegation Group | |||||||||
| 1 | Hibernian | 0 | 0 | 0 | 0 | 44 | 51 | -7 | 39 |
| 2 | Motherwell | 0 | 0 | 0 | 0 | 46 | 51 | -5 | 37 |
| 3 | Aberdeen | 0 | 0 | 0 | 0 | 35 | 49 | -14 | 35 |
| 4 | St Johnstone | 0 | 0 | 0 | 0 | 24 | 46 | -22 | 31 |
| 5 | Ross County | 0 | 0 | 0 | 0 | 32 | 56 | -24 | 30 |
| 6 | Livingston | 0 | 0 | 0 | 0 | 22 | 59 | -37 | 18 |
| First Phase | |||||||||
| 1 | Celtic | 33 | 24 | 6 | 3 | 80 | 26 | 54 | 78 |
| 2 | RangersRangers | 33 | 24 | 3 | 6 | 72 | 23 | 49 | 75 |
| 3 | Hearts | 33 | 19 | 5 | 9 | 46 | 34 | 12 | 62 |
| 4 | Kilmarnock | 33 | 13 | 12 | 8 | 43 | 34 | 9 | 51 |
| 5 | St Mirren | 33 | 12 | 7 | 14 | 38 | 43 | -5 | 43 |
| 6 | Dundee | 33 | 10 | 11 | 12 | 44 | 54 | -10 | 41 |
| 7 | Hibernian | 33 | 9 | 12 | 12 | 44 | 51 | -7 | 39 |
| 8 | Motherwell | 33 | 8 | 13 | 12 | 46 | 51 | -5 | 37 |
| 9 | Aberdeen | 33 | 8 | 11 | 14 | 35 | 49 | -14 | 35 |
| 10 | St Johnstone | 33 | 7 | 10 | 16 | 24 | 46 | -22 | 31 |
| 11 | Ross County | 33 | 7 | 9 | 17 | 32 | 56 | -24 | 30 |
| 12 | Livingston | 33 | 3 | 9 | 21 | 22 | 59 | -37 | 18 |
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