The Magpies won plaudits for the quality of their overall display at Selhurst Park on Saturday as a commanding performance produced an emphatic Premier League win.
Cabaye, back after a one-match ban, notched his fourth goal of the season in the first half while Anita turned in another tenacious showing in central midfield.
But with Stoke up next at St James' Park on Boxing Day, both players admired their team-mates' ability to roll their sleeves up and get stuck in against one of the struggling sides.
Cabaye said: "To be in the team and play like that is always a good feeling.
"It was a small pitch, a small stadium and a big atmosphere. For my goal, Moussa (Sissoko) loves that little pass and I'm always thinking about trying to be in the right position and hit the target. Now I just want to keep scoring!
"But we just want to think about the next game and focus on that, because if we think about the end of the season such as the Europa League or something more, it might be difficult to stay focused.
"The next battle is going to be hard, Stoke City at home. We just want to get three points and stay at the top of the league."
Anita added: "We have a good ambience in the team and you can see that when we get results. Palace need the points but we were ready for a battle today, and we won."
On playing alongside Cabaye, the Holland international said: "It's always good to have Yohan in the team. We connect well in midfield."