Di Canio was furious at the way his team were defeated by two second-half goals and insists he will have his squad in for Sunday morning training.
The Italian said: "I would like to fine my players but it may not be possible because they have too much protection. When I tell players they are average they get angry, but that was the case in this game. Now the club has to say sorry to everybody because they damaged themselves."
Macclesfield goalkeeper Lance Cronin made good saves from Raffaele de Vita, Andy Williams and Gary Roberts but Swindon paid for their wastefulness.
Tony Diagne put Macclesfield ahead with a fierce 35-yard free-kick into the top corner after 63 minutes and after Aden Flint was sent off, the win was confirmed when Robins substitute Louis Thompson scored an own goal.
Town were narrowly beaten by Aston Villa in the Capital One Cup in midweek and Di Canio admitted he hardly recognised his team.
He added: "For three days after Villa I was happy. Now I am angry. Tomorrow (Sunday) at 7.30 we will be training at Liddington and Di Canio will be the first to arrive. I know how to manage my players. Sometimes they think they are Barcelona players, but they are not."
Macclesfield boss Steve King said: "This is massive for us and our fans. Look at the gulf between the clubs. Last year we were in the same division but now they are looking to get into the Championship.
"Days like this you can only dream about and we will all savour it while we can. I am proud of the team and my players because they gave me everything. We came under a lot of early pressure and held out but once we went ahead I felt we were the better team and I had no doubts we would go on and win.
"We can think about getting to the third round and perhaps Manchester United away but just to get to the second round is an achievement and we shall enjoy our day."