Albion boss Micky Adams has challenged former Seagull Andy Ritchie and his Oldham side to cope with the pressure of being the new Second Division leaders.
Saturday's 1-1 draw at Cardiff stretched the Seagulls' unbeaten September League sequence to six matches.
Oldham beat Notts County 4-1 at home to knock them down into second place on goal difference.
"We have lost top spot, so we'll have to chase somebody else now," Adams said.
"Let's see how they cope with the pressure. I think my lads have coped with it admirably."
A first-half blunder by Cardiff fullback Rhys Weston gifted Bobby Zamora his eighth goal of the season.
Paul Brayson equalised for the Welsh giants with ten minutes left to repeat the result for Albion at Wycombe Wanderers four days earlier.
"Sometimes it's better to win one and lose one, but we have shown the mental strength to go away and perform well and the character," said Adams.
"We have only picked up two points, but we are on an unbeaten run and long may it continue.
"Cardiff is a difficult place to play. It's an intimidating atmosphere, particularly for the supporters, but we didn't let that affect us.
"I was delighted with the performance. It was a very competitive game, as you would expect, and we are slightly disappointed we didn't come away with the three points."
Cardiff boss Alan Cork, Adams' former assistant and godfather to his baby son, was dissatisfied with a point, which leaves the big-spending Welshmen still struggling at the wrong end of the table.
"We dominated the game and deserved more," Cork complained.
"Brighton only had one shot and they scored. It was a mistake by us, but that's life.
"We controlled a lot of the first half, but credit to them. Micky is doing a good job, which is what I would expect because he is a good manager. They are well organised and very hard to beat."
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