The Gunners were pegged back twice by the Seagulls after Olivier Giroud struck twice, before Theo Walcott popped up in the 85th minute to seal progression to the fifth round
The hosts levelled twice to cancel out Olivier Giroud's double but Theo Walcott grabbed the winner in the 85th minute to secure a spot in the fifth round.
"Brighton made it very difficult for us and were sharper than us in the first half. They had a great spirit today," Wenger told Sky Sports.
"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 chose to rest several first-team regulars and admitted his concern that the decision could have come back to haunt him.
He added: "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."
The 63-year-old also singled out Giroud for praise, with the France international having scored four goals in two games, and Wenger insisted he was not in a rush to find a new striker with the £13 million man finding form.
"It's good for his confidence, He's scored four goals this week and he had a few more chances today," the manager said.
"Giroud gets there. He has a presence in the box. He is dangerous and his physical presence was very important today.
"You do not find them in the street, strikers who can play for us. We have strength in our team. It is difficult in January.
"Realistically, I cannot tell you I will sign anyone tomorrow, or Tuesday, as we are not close to doing it."