The Stadium of Light club's owner, Ellis Short, on Saturday evening decided to sack Martin O'Neill after a defeat by Manchester United earlier in the day left them in further Premier League relegation danger.
Di Canio was swiftly named as the new boss and the Italian's arrival has been seen as somewhat of a surprise given his only previous experience was the two years he spent with Swindon Town, who he guided to promotion to League One.
And Neville believes there is an immense amount of uncertainty surrounding the arrival of Di Canio, who has also been having to respond to criticism of previous allegedly racist behaviour.
"I do not know what is going to happen," Neville said on Monday Night Football. "It is very un-Sunderland-like when you think of [previous managers] Peter Reid, Niall Quinn, Roy Keane, Steve Bruce and Martin O'Neill. You could argue it is very different from those appointments.
"It is a change of tact. Maybe that is something Ellis Short was very conscious of and wanted to do. It is a risk but life is about risks.
"We will only know in a few weeks' time. I have to say, the whole atmosphere on Saturday looked a little bit dejected. In some ways, Di Canio coming in will give Sunderland a massive lift and he did well at Swindon."
There have been 28 occasions when Premier League sides have changed their manager after Christmas and it has had mixed results, with 14 teams being relegated and 14 avoiding the drop.
No side outside the relegation zone have ever changed their manager after the festive period and then gone down, and Sunderland will hope that statistic continues.
But Neville also thinks boyhood Sunderland fan O'Neill was not offered enough time, having only taken over at the Stadium of Light in December 2011.
"I would never advocate a change being made," said Neville. "I would never sit here and think a manager who was appointed 15 or 16 months ago as a messiah goes to becoming the villain all of a sudden and is responsible for everything.
"He has spent some money at the start of the season but it is no time in the job. It is no time to build what he wanted to create up there.
"Ellis Short's decision, I think, is gut instinct. Maybe he has not liked things he has seen or heard in the past weeks. But, to me, he has thought, 'I'm going for it'. And has he gone for it!"