The Seagulls created chances and missed a penalty against David Moyes team but goals from Iliman Ndiaye and James Garner sealed the win for the Toffees.
Brighton have just one point from their first two Premier League matches and are back in action on Wednesday in the Carabao Cup at Oxford United.
Fabian Hurzeler will look to make plenty changes at the Kassam Stadium and then hope to fire back in the Premier League as Manchester City visit the Amex Stadium on Sunday.
So how can Hurzeler get the spark back in the team and what is the best midfield option as Carlos Baleba continues to struggle? Here’s the Brighton line up Fabian Hurzeler needs to try...
9. Yankuba Minteh - RW
Brighton's best player at Everton and always likely to cause problems with his pace, skill and power. Photo: Clive Mason
10. Matt O'Riley - No 10
The Danish attacker was criticised for missing a chance at Everton but I quite like him in the No 10 role. Takes up good positions and capable of picking the right pass. Photo: Michael Regan
11. Kaoru Mitoma - LW
If anyone is capable of bringing spark back to Brighton, then it's Mitoma. So unlucky not to score at Everton and surely his goals and assists will come in the next few matches. Photo: Clive Mason
12. Georginio - CF
Missed the Everton match with a "minor issue" and is expected to return soon... hopefully in time for the Manchester City match on Sunday. The Seagulls need him. Photo: Ryan Pierse