The Swans defeated Manchester City 1-0 on Sunday to move 14 points off the drop zone.
"We're not safe mathematically so we've got to keep going," Monk said.
"But even if we were on 40 points now, we wouldn't settle for just being safe, that's not how we work.
"If we don't stay up now we all deserve shooting in the head."
Swansea are 11th in the league with 36 points from 28 games.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Sheffield UnitedSheff Utd | 20 | 13 | 5 | 2 | 28 | 11 | 17 | 42 |
| 2 | Leeds UnitedLeeds | 20 | 12 | 5 | 3 | 36 | 14 | 22 | 41 |
| 3 | Burnley | 20 | 10 | 8 | 2 | 24 | 7 | 17 | 38 |
| 4 | Sunderland | 20 | 10 | 7 | 3 | 29 | 15 | 14 | 37 |
| 5 | Blackburn RoversBlackburn | 19 | 10 | 4 | 5 | 23 | 17 | 6 | 34 |
| 6 | West Bromwich AlbionWest Brom | 20 | 7 | 11 | 2 | 23 | 14 | 9 | 32 |
| 7 | Middlesbrough | 20 | 9 | 4 | 7 | 34 | 25 | 9 | 31 |
| 8 | Watford | 19 | 9 | 4 | 6 | 27 | 25 | 2 | 31 |
| 9 | Swansea CitySwansea | 20 | 7 | 6 | 7 | 21 | 19 | 2 | 27 |
| 10 | Norwich CityNorwich | 20 | 6 | 8 | 6 | 35 | 30 | 5 | 26 |
| 11 | Bristol City | 20 | 6 | 8 | 6 | 25 | 25 | 0 | 26 |
| 12 | Sheffield WednesdaySheff Weds | 20 | 7 | 5 | 8 | 23 | 29 | -6 | 26 |
| 13 | Millwall | 19 | 6 | 7 | 6 | 20 | 17 | 3 | 25 |
| 14 | Derby CountyDerby | 21 | 6 | 6 | 9 | 26 | 26 | 0 | 24 |
| 15 | Preston North EndPreston | 20 | 4 | 10 | 6 | 20 | 26 | -6 | 22 |
| 16 | Luton TownLuton | 20 | 6 | 4 | 10 | 23 | 35 | -12 | 22 |
| 17 | Coventry CityCoventry | 20 | 5 | 6 | 9 | 25 | 29 | -4 | 21 |
| 18 | Stoke CityStoke | 20 | 5 | 6 | 9 | 21 | 26 | -5 | 21 |
| 19 | Queens Park RangersQPR | 20 | 4 | 9 | 7 | 20 | 26 | -6 | 21 |
| 20 | Oxford UnitedOxford Utd | 19 | 4 | 6 | 9 | 20 | 30 | -10 | 18 |
| 21 | Portsmouth | 19 | 3 | 8 | 8 | 21 | 34 | -13 | 17 |
| 22 | Cardiff CityCardiff | 19 | 4 | 5 | 10 | 17 | 30 | -13 | 17 |
| 23 | Plymouth ArgylePlymouth | 19 | 4 | 5 | 10 | 19 | 40 | -21 | 17 |
| 24 | Hull City | 20 | 3 | 7 | 10 | 18 | 28 | -10 | 16 |
| > Championship Full Table | |||||||||
