Arsene Wenger will become the most successful manager in FA Cup history if the Gunners retain the trophy at the end of the season but he is not looking too far ahead.
"We have a goal [to win the trophy], of course, but it's such a long way to go and you've seen today again the tie is not predictable until the last minute," the Frenchman said.
"You have to fight for it, we are ready for a fight."
Hughton, who succeeded Sami Hyypia as Brighton boss on New Year's Eve, was pleased with his players' response after going two goals behind but not with their start to the game.
"I'm delighted with the way we finished, but I'm not happy with the first-half performance because I felt an Arsenal team coming here -- as good as they are -- we were second best certainly for the first half an hour," he said.
"I'm really delighted with what we showed at the end. I think at the end of the game what you want is a home crowd to see a Brighton team that has had a real go and I think they've seen that."