Wenger had made several changes from the side which thumped West Ham 5-1 in the Barclays Premier League on Wednesday night, and started with England duo Jack Wilshere and Theo Walcott on the bench.
"Brighton made it very difficult for us and were sharper than us in the first half. They had a great spirit," Wenger said. "But in the end we had that little bit of extra quality to get us through. We did our job, but needed to fight until the end."
Wenger admitted his team selection could have come back to haunt him.
He said: "That is a gamble you take and you know it can backfire. You have to rotate knowing that if it doesn't work you will be accused of having made the wrong decision."
Olivier Giroud, who scored twice in midweek, hit another brace for the Gunners and the France international offered Arsenal a real physical presence at the spearhead of their attack.
Wenger said: "It's good for his confidence. He's scored four goals this week and he had a few more chances.
"Giroud gets there. He has a presence in the box. He is dangerous and his physical presence was very important."
Brighton manager Gus Poyet, meanwhile, felt his side should not be too despondent despite not earning a replay from all of their hard work, which was produced despite losing both captain Gordon Greer and winger Will Buckley, who had stretched Arsenal down the right, to injury.
"It is a funny feeling because we are more disappointed than we should be in the dressing room. It is like we had lost a final," Poyet said. "We had the chance to do something special, but when you lose players like we did to injury, against players like the quality of Arsenal, there is not much you can do."
- Sports & Recreation
- Barclays Premier League
- Jack Wilshere