Petersfield confirmed Robson quit the struggling club after the opening 45 minutes of their defeat to Kidlington on Saturday.
Robson has previously held roles at Gosport Borough, Winchester City, Andover Town, Blackfield and Langley, Worthing and Dover.
With the Rams 3-0 down after the opening 45 minutes and relegation from the Evo-Stik League Southern Central virtually confirmed, Robson decided he'd had enough.
Petersfield showed more fight in the second half as the game ended 4-2, but the result still left them on nine points, 20 behind the next team at the bottom of the table.
The Hampshire club have picked up just one point in their last 15 matches.
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