Roberto Martinez heaped praise on Ross Barkley after the youngster's matchwinning free-kick at Swansea.
Barkley's stunning strike proved the difference between the sides after Seamus Coleman's brilliant drive had put the Blues ahead.
The Swans had been level but Martinez agreed that his side were worthy of all three points.
He told evertontv: "In the second half we had more intent when we were on the ball. I don't underestimate the size of this result at all. It is a magnificent three points and it's down to the character, resilience and the belief that the players had.
"You look at the quality of Ross Barkley and the way that Seamus Coleman has a massive impact in the final third. It's very pleasing.
"We had been in situations earlier in the game where we were missing the final pass or a bit of composure, so it's important to have players to control the moment and be ready to get the winning goal.
"The technique (for Barkley's goal) was as good as it gets. To have that sort of ability is extremely pleasing. To see him developing is a joy and he is a phenomenal ambassador for our football club."
Martinez also reserved words for the thousands of Evertonians who had braved the harsh Welsh weather to back their side just before Christmas.
He added: "The support was incredible. We scored the two goals in front of them and their support was magnificent."