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.
However, eventually the Gunners had enough to see off the npower Championship side, who had twice levelled, with substitute Walcott netting a late winner to send Arsenal into tomorrow's draw.
"Brighton made it very difficult for us and were sharper than us in the first half. They had a great spirit today," 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."