Alan Pardew's side battled back from 3-0 down to lose 3-2 but they were completely outplayed in the first half at Goodison Park.
Remy scored the final goal of the game as Newcastle staged a late rally to try and secure a point but the France international admits they must improve for their supporters when they face Cardiff on Saturday.
"It was a long journey last night for them," he told the Newcastle Chronicle.
"The group is disappointed as much as them but the fans still supported us all the game.
"We heard them a lot in the second half. They continued to support the team. I'm sure we'll do better at Cardiff for them.
"The difference between the first half and the second half was like night and day. The gaffer changed two players, and there was a big difference between the two halves.
"We could have done better for the goals. It's difficult when you concede three goals.
"After that, we scored two goals, but it wasn't enough. We were all disappointed."