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...
Brighton boss Fabian Hurzeler saw his side suffer a 2-0 loss against Everton
1.
Brighton boss Fabian Hurzeler saw his side suffer a 2-0 loss against Everton Photo: Ryan Pierse
The Dutch goalkeeper perhaps should have saved Everton's second goal but he remains Hurzeler's trusted No 1.
2. Bart Verbruggen - GK
The Dutch goalkeeper perhaps should have saved Everton's second goal but he remains Hurzeler's trusted No 1. Photo: Michael Regan
Brighton's experienced and reliable defender could return to the right back slot, which should allow Mats Wieffer to go to his preferred midfield role
3. Joel Veltman - RB
Brighton's experienced and reliable defender could return to the right back slot, which should allow Mats Wieffer to go to his preferred midfield role Photo: GLYN KIRK
The Brighton skipper has looked sharp of late and keeps his spot despite competition from Coppola and Boscagli
4. Lewis Dunk - CB
The Brighton skipper has looked sharp of late and keeps his spot despite competition from Coppola and Boscagli Photo: Clive Mason