Chelsea were held to a goalless draw at Goodison Park which completely killed their title chances.
The Blues were without Alvaro Morata, who was suspended after picking up his fifth yellow card of the season.
And they looked incredibly short up top as they lacked the clinical edge, which frustrated Rudiger.
“Of course it’s very disappointing because I think we were the better team and we had a lot of chances to score,” Rudiger said.
“But you have some days when it’s like that.
“You can even play for maybe three hours and you wouldn’t score.
“We needed the three points so we have to keep going.
“We played a good match but we were just unlucky.”
Meanwhile, fellow defender Marcos Alonso echoed Rudiger’s remarks.
“We were very unlucky not to win after controlling the whole game and having a lot of chances,” he said.
“But we take one point, it is what it is, very disappointing.
“We knew it was going to be tough and as the game was passing it was getting harder because they were defending closer to their goal.
“The performance wasn’t bad, we just need to be more clinical.”