Di Canio resigned as Town manager last month, citing broken promises over the club's decision to sell Matt Ritchie to AFC Bournemouth.
Watkins, who stepped down from his position last week, has revealed that Di Canio was demanding to work with.
"Paolo Di Canio was a challenge - no question," Watkins told BBC Wiltshire. "He was demanding to work alongside and had his own style. He spoke very much from the heart and along the way created a bit of collateral damage that I had to repair.
"Often I refer to it as management by hand grenade. Paolo would chuck a hand grenade and I would do the repair work at the end, like the Red Cross.
"Paolo re-energised the town, re-energised the football club and got us promoted. It's just disappointing he didn't stay to see the job done."
Di Canio led Swindon to the League Two title last season.