League Two Grimsby have defeated five clubs above them in English football's structure - Plymouth, Cambridge, Burton, Luton and Southampton - to secure a last-four clash with the high-flying Seagulls.
De Zerbi has warned of the threat Grimsby pose after they beat Premier League club Southampton in the previous round.
"It will be a difficult game," the Italian said on Friday. "But I want (the) players to give 100 percent of possibilities.
"I want our fans to support our players because Sunday is a difficult game. We have to not think, 'We are Brighton from the Premier League and Grimsby are in the fourth division', because we would make a big mistake."
"We have to play seriously, because for us it is a big opportunity to go to Wembley," added De Zerbi, whose side are seventh in the Premier League.
Brighton will be without right-back Tariq Lamptey, who suffered a knee injury against West Ham earlier this month, while Adam Lallana and Jakub Moder remain sidelined.
