Twice in south London Everton surrendered their lead but neither time were they deterred and they finally nicked it with a goal from Idrissa Gueye four minutes from the end.
Dyche, whose side beat West Ham at the London Stadium on their last Premier League away day, said he saw clear signs that his players are forging a mentality to win consistently away from Goodison Park.
“Obviously topsy-turvy,” said Dyche. “We started so well, with a fantastic goal. They responded with a moment we should have dealt with earlier. They get a soft penalty from our point of view.
“Then really it was a strange game after that. I don’t think anyone really gripped the first half, and second half (Palace) did. I thought they were very good. I think we had to work very hard.
“I think the mentality I’m trying to work with the players on is the belief in finding different ways of winning games, and I think we’re showing that.
“We had to do it last week against Brighton, so nearly won but got a good point. Then coming (to Palace) today.
“Away form here was a big question mark when got here. We’re beginning to change the mentality towards these games. That was on show today.”
Vitalii Mykolenko headed in Jack Harrison’s cross after only 55 seconds but Eberechi Eze, on his first start since returning from a hamstring injury, levelled from the penalty spot four minutes later.
The hosts could not hold on to a point, though, as Gueye struck late to win it after latching on to Doucoure’s excellent through-ball.
Mykolenko, who had a hand in Doucoure’s goal, put in one of his best performances in an Everton shirt and Dyche said he felt the Ukrainian’s progression encapsulated his side’s improved approach in recent weeks.
“He’s beginning to mature into himself really as a player and in his Everton career,” he said. “I think he can defend, he’s beginning to show that he can go forwards, he wants to get into the right areas.
“It’s a fantastic header and he’s nearly got a brace with a lovely strike, a controlled effort at goal.”
Palace boss Roy Hodgson reflected on a match that ultimately slipped away from his side despite a gallant effort to twice recover from falling behind.
“I’m sad, I’m frustrated,” he said. “Early goals in each half, we had to come from behind twice.
“We had to work very hard to come from behind twice and put in a very good effort. We had a lot of the ball and worked hard to create those chances.
“To then concede a third goal and lose the game, that’s hard to take.”