The Eagles manager annoyed some Palace fans following their 3-0 defeat at the Amex in March when he dismissed the derby, between two clubs almost 50 miles apart, as "nonsense".
But ahead of Friday night's Championship play-off semi-final first leg between the sides at Selhurst Park, Holloway has been left in no doubt about the importance of the fixture.
"All I said was that, with the geography, I was surprised how much they hated each other," he said.
"It doesn't mean that I don't understand how they really do not like each other, and I have got no problem with that.
"This week one bloke collared me and said 'don't you understand yet, don't you understand why we hate them?' I did anyway but don't you think I go about my job in a professional manner and get my lads to want to win? As if I didn't."
The feud stems from a series of controversial clashes between the sides as they both went for promotion in the late 1970s under their charismatic rival bosses Terry Venables and Alan Mullery.
And as the Eagles and the Seagulls prepare to meet again, Holloway has called for one of his players to write themselves into Palace folklore.
"I don't think either set of supporters would fancy this game," he added. "They would prefer it to be the final - and even that would be their worst nightmare.
"Ask a Palace fan. Who would you hate to lose to the most? Brighton. That is what the play-offs throw up.
"I'll be challenging one of my lads to be a hero and a Palace legend. But if you miss and they go through you could be the worst Palace player ever - because it's Brighton!
"Whatever happens, I will be one of two things. But I am ready for whatever that is because I am only going to do my best and so are my lads."