Madrid came out on top despite being second best at times, but the Spanish capital club still remains five points behind top two Barcelona and Atletico Madrid.
Ancelotti credited Valencia's spirited performance to the presence of their new coach, Juan Antonio Pizzi, but praised Real's battling display believing that next year could be momentous for the club.
"Five points is quite a lot but I believe today's match was very important, because we had a lot of pressure because we started the game 8 points off the leaders," Ancelotti said.
"I think we have lost some points looking for a way of playing, nowadays we like to battle so I think 2014 could be a great year for Real Madrid.
"At this moment of the season the table standings is very clear but, as I said, I am really looking forward for the second part of the season."
Madrid are next in action in the league on January 6 at home to Celta Vigo, with La Liga off due to the winter break.
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