Theo Walcott grabbed an 85th-minute winner to send Arsenal into the fifth round, but Wenger admitted that it was difficult for his side.
The Frenchman praised Brighton's effort, insisting that they were the better side in the first half, but claimed that his side's "extra quality" helped them through.
"Brighton made it very difficult for us and were sharper than us in the first half. They had a great spirit today," said Wenger.
"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."
Arsenal currently sit in sixth place in the Premier League.