Theo Walcott's 85th minute winner sent Arsenal into the fifth round of the FA Cup after Brighton had twice drawn level following goals from Olivier Giroud.
Wenger acknowledged Brighton were the better team in the first half and was pleased with how his players responded to the challenge against a Championship club.
"Brighton made it very difficult for us and were sharper than us in the first half. They had a great spirit today," said the Arsenal boss.
"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, saying: "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."
Giroud has slowly grown in stature since his summer move from Montpellier and followed up a double against West Ham in midweek with another brace against Brighton.
"It's good for his confidence," added Wenger. "He's scored four goals this week and he had a few more chances today.
"Giroud gets there. He has a presence in the box. He is dangerous and his physical presence was very important today."
Arsenal have yet to move in the January transfer window, and Wenger insisted he was in no rush to panic buy ahead of the deadline despite being linked with a string of players across Europe.
He said: "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."