Saints remain in the bottom three after the result but Adkins believes that his side are showing the right attitude to improve.
"The supporters have been great, the players outstanding," he told BBC Sport.
"We're in the toughest league in the world and intend to stay there."
Southampton are 19th in the table with five points from 11 games.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 6 | 5 | 0 | 1 | 12 | 2 | 10 | 15 |
| 2 | Manchester CityMan City | 6 | 4 | 2 | 0 | 14 | 6 | 8 | 14 |
| 3 | Arsenal | 6 | 4 | 2 | 0 | 12 | 5 | 7 | 14 |
| 4 | Chelsea | 6 | 4 | 1 | 1 | 15 | 7 | 8 | 13 |
| 5 | Aston Villa | 6 | 4 | 1 | 1 | 12 | 9 | 3 | 13 |
| 6 | Fulham | 6 | 3 | 2 | 1 | 8 | 5 | 3 | 11 |
| 7 | Newcastle UnitedNewcastle | 6 | 3 | 2 | 1 | 8 | 7 | 1 | 11 |
| 8 | Tottenham HotspurSpurs | 6 | 3 | 1 | 2 | 12 | 5 | 7 | 10 |
| 9 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 10 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 11 | Bournemouth | 6 | 2 | 2 | 2 | 8 | 9 | -1 | 8 |
| 12 | Brentford | 6 | 2 | 1 | 3 | 8 | 10 | -2 | 7 |
| 13 | Manchester UnitedMan Utd | 6 | 2 | 1 | 3 | 5 | 8 | -3 | 7 |
| 14 | West Ham UnitedWest Ham | 6 | 1 | 2 | 3 | 6 | 10 | -4 | 5 |
| 15 | Ipswich TownIpswich | 6 | 0 | 4 | 2 | 5 | 10 | -5 | 4 |
| 16 | Everton | 6 | 1 | 1 | 4 | 7 | 15 | -8 | 4 |
| 17 | Leicester CityLeicester | 6 | 0 | 3 | 3 | 8 | 12 | -4 | 3 |
| 18 | Crystal Palace | 6 | 0 | 3 | 3 | 5 | 9 | -4 | 3 |
| 19 | Southampton | 6 | 0 | 1 | 5 | 3 | 12 | -9 | 1 |
| 20 | Wolverhampton WanderersWolves | 6 | 0 | 1 | 5 | 6 | 16 | -10 | 1 |
| > Premier League Full Table | |||||||||
