Everton boss Sean Dyche was delighted with victory at Brighton.
The Toffees meet Prem leaders Manchester City today.
In his match programme notes, Dyche wrote: "The most pleasing part of the performance from my perspective was that we didn't wait for anything to happen. Brighton play a very particular way, creating two boxes in midfield and they look to move you around with clever movements. We devised a game plan that required patience, focus and being clinical in the right moments and the players deserve credit for showing all of those things from the first whistle.
"There was a real clarity to our work and a mentality to take the game on to win. We must continue that as we look forward.
"The general reaction after the Brighton game was one of surprise and while I understand that given the emphatic scoreline which is a big one for any team in the Premier League, before you factor in we were playing a confident side chasing European football I saw signs of that performance in the previous game against Leicester City.
"There has been a lot of noise about Everton playing away from home over the past couple of years and that is justified given the record. But, as a group, we've been keen to correct that. We've started to build a different mentality and there have been signals that our performances on the road have been getting stronger. Some wins got away from us the 2-2 draws at Nottingham Forest and Leicester City as examples but the commitment and intent has been there for a while.
"It was pleasing, then, to see that all come together at Brighton, because it is wins that really reinforce that feeling of confidence and the belief we are heading in the right direction.
"With all of that said, it was just another step."