The Seagulls manager was delighted to see a youthful Albion team work hard and create plenty of chances against a spirited Swansea.
The third round tie finished 2-0 at the Falmer Stadium, with Brighton set to take on Leicester City in the fourth round.
Potter said, per The Argus: "Delighted to go through, it was a tough game. Two teams going at it. Swansea contributed really well, I thought they were fantastic as well.
"Really pleased with our players, I thought the attitude was great. Commitment to the game, showed good respect to the opponents, worked really hard and obviously Aaron's two finishes made the difference."
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