The Robins tested themselves against higher division opposition in last year's competition, beating Bristol City before being knocked out by Southampton in the second round.
Di Canio told the club's official website: "Obviously I am very happy with the draw. Last season we started very well in the cups against higher-division opposition and we now have that opportunity again.
"It will be special this year because the game is played before the league season begins. It will be an important test against a good footballing side.
"Brighton will be a good chance to see how the players integrate and play together as a group. Only through victories can we build the belief and it should be an exciting match.
"We want to give satisfaction to our supporters after the summer break and hopefully there will be a big crowd at the County Ground so we can start the new season together."