The Brazilian prodigy was the subject of a tug of war between the two arch-rivals over the summer, before eventually deciding on a 57 million-euro switch to Camp Nou.
After netting the opener in his first appearance against Los Blancos, the 21-year-old expressed his delight at how well his first appearance in the famous fixture had gone.
"I had seen many Clasicos, it was great to play one," Neymar told reporters.
"It was so hard against a great team. I'm so happy about the victory, the team and the goal. Cristiano [Ronaldo] is a great player, but we have also many good players."
Teammate Alexis Sanchez was introduced by Gerardo Martino in the second period, and effectively won the game for Barca with a sublime chip over Diego Lopez.
"I'm very happy about the goal and the match. I saw Diego Lopez had advanced too much so I tried to hit the ball over him," the Chilean said.
"This is a very beautiful match that everybody wants to play. Real Madrid is a very hard team to beat, it was not easy."
The Spanish champions now sit six points ahead of third-placed Madrid in la Liga.