Exeter manager Paul Tisdale felt a draw would have been a fair result, but took his side's 2-1 home defeat defeat thanks to Ashley Barnes' late winner on the chin.
Barnes, a 63rd-minute substitute, first set up the Seagulls` equaliser - Richard Logan had headed Exeter into a first-half lead - when he crossed for Glenn Murray to head home and won it for the Seagulls in the last minute when he slotted home at the far post from Elliott Bennett's cross.
Tisdale said: "It was sickening to lose that way, but these things happen. We've had our fair share of late goals and you have to take it when it happens the other way.
"I don't often say it, but I think we were a little unlucky. That's not to say they were lucky because Brighton played extremely well.
"It was a very open game and when it got to the death there, I thought if anyone was to concede a goal they would feel aggrieved because it was a terrific game, a fantastic game of football and a draw would have been the fair result.
"We've played the top two teams in the league this weekend and I think we've given a very good account of ourselves."