Jones exited with a hip flexor injury, while Sanu hurt his hamstring.
Jones was injured in the second quarter. He appeared to try to lobby coach Dan Quinn to put him back into the game before exiting. He entered the contest already battling a back injury suffered in last week's victory over the Detroit Lions.
Quinn said afterward that Jones "definitely" wanted to get back in the game after suffering the injury but did not have his usual explosiveness, which is why he was held out.
"He had trouble just exploding, and if he can't be him, that's a unique thing for him," Quinn said. "The speed, the explosiveness -- so when he wasn't able to do that, that's when we had to pull him. He definitely wanted to go."
Jones had three catches for 30 yards on four targets in the first quarter.
The Falcons also ruled out defensive lineman Jack Crawford with a biceps injury, of which a source said, "It doesn't look good." Crawford has an MRI scheduled for Monday morning.