"The sole focus of everyone for the next seven games will be to ensure we gain enough points to maintain our top-flight status.
"I think that the chances of that are greatly increased with Paolo joining us."
Fans are likely to be divided over the arrival of 44-year-old Di Canio, who is remembered as much for pushing over a referee as for his sportsmanship during his playing days in England.
His appointment prompted former British foreign secretary David Miliband to quit the Sunderland board, releasing a statement saying the move was due to "the new manager's past political statements".
Di Canio drew outrage in 2005 when he celebrated his side Lazio's derby win over AS Roma with a fascist-style salute.
He received an 11-match ban in 1998 for shoving referee Paul Alcock to the ground after being shown a red card while playing for Sheffield Wednesday.
The Italian was idolised by West Ham fans and scored a spectacular volley against Wimbledon that was voted goal of the season.
He also picked up a fair play award for catching the ball - rather than shooting into an open goal - so that injured Everton goalkeeper Paul Gerrard could receive treatment during a league game.
Former striker Di Canio, who inherits a team hovering one point above the relegation zone, landed his first job as a coach when he was appointed at Swindon in 2011.
He guided the club to the fourth-tier title a year later and said he was prepared to eat into his savings to fulfil his ambition of taking them into the second tier.
He left Swindon on February 18 after a typically roller-coaster time with the club.
His passion often boiled over into rows with his players and this season he antagonised fans by telling those unhappy with his decisions to go and support local rivals Oxford United.
Di Canio's first match in charge of his new club is next Sunday's trip to Chelsea.
O'Neill was dismissed on Saturday after the club's 1-0 defeat by league leaders Manchester United which left the north- east club without a win in eight games.
They have 31 points from 31 games, one point more than 17th- placed Wigan Athletic who have played one match fewer and a point more than 18th-placed Aston Villa who have played the same number of games.
"Our fans have shown tremendous patience and understanding this season," chairman Short said.
"They have continued to back the team in huge numbers, both home and away, and that is something that continues to inspire all of us in our drive to give them the successful club they deserve. That remains our primary aim."