Di Canio knows he has yet to convince some after his wholesale summer changes - including an entire team-full of new signings, a room-key lottery on away trips and bans on everything from Marmite to drinks with ice cubes.
Di Canio insisted: "I don't mind having people against me because it is very satisfying when you win at the end and prove them wrong.
"What is important is that you don't give up. Don't listen to the ones who keep putting the club down - they are like crows. Everyone should stay positive because we are going to have a very good season - I'm sure about that."
Di Canio completed his 11th new signing this week with the addition of Greek midfielder Charis Mavrias from Panathinaikos, although he is unlikely to feature in the Italian's plans to face the Saints.
Craig Gardner's return from suspension gives Di Canio defensive options but he is likely to keep faith in last week's line-up, with Ondrej Celustka impressing at right-back and Valentin Roberge forgiven for the blunder that led to Fulham's winning goal.
Striker Steven Fletcher is still some weeks away from a first-team return but continues to make good progress with his ankle injury, while Wes Brown is nearing full fitness but will not be rushed back from his knee problem.
Jozy Altidore will get another chance to impress up front after an encouraging debut which Di Canio believes only began to hint at the quality the United States international - who scored a hat-trick on international duty less than two weeks ago - can add to his forward line.
Di Canio added: "He is a fantastic player who proved himself straight away but he can do much better.
"In modern football you have a lot of good athletes but maybe they don't have a good touch, but he is different from those players because he is good at everything.
"He can attack the space, hold the ball and take on his opponents and maybe strike on goal, so I'm not worried. He is 23 and very mature for his age, and I'm very happy with him."