Try as they might, the Eagles were unable to break down the stubborn resistance provided by the Toffees, who finished the game with 10 men after Mason Holgate’s late second yellow card.
The point does, however, stretch Palace’s unbeaten run to four games and move them nine points clear of Everton and the Premier League drop zone, with just six games left to play.
Eze said: “It was a tough game. There wasn’t really much in it – it was scrappy.
“I think we tried as much as we could to create chances and to get balls into their box, but it was a difficult one.
“With the way they play, it’s difficult to get the ball down – they don’t give you much time. We worked hard. We did everything we could, and it’s positive getting a point.
“We’ve worked hard to be in this position. We want to keep on putting in performances and getting points every single game. That’s the main objective for us.”
With Palace making yet another bright start to the second-half, Eze thought he had given Palace the lead with a cute lobbed finish, only to be denied by the linesman’s flag and VAR.
Eze reflected: “It was close, but that’s how these games are. Small chances, not really creating as much as we like… but again, there are positives.
“[At half-time] the message was to keep going, not to allow them too many chances, not too many free-kicks, and not to let them take charge of the game.
"I think we did that. We stayed in it the whole way through and to get a point is positive. We can build on it.
“Against 10 men, you want to create, get the ball into the box as much as possible and stay in their half, but honestly, the way they play, it’s very difficult. They don’t allow you anything.
"We just have to keep going.”