Both men were withdrawn from their respective national teams after picking up knocks during the 1-1 draw with Liverpool last weekend.
Benitez stated that Ritchie was feeling the effects of fatigue after a rigorous run of games, while Atsu suffered a knee injury.
“Matt Ritchie has been playing too many games,” said Benitez, according to the Shields Gazette. “He was working very hard and has had a little bit of discomfort lately.
“There have been a few little things he has been talking about with the doctor. It was better that we didn’t take a risk.”
On Atsu, Benitez added: “He has a little bit of discomfort in his knee and we have to manage it carefully.”