The midfielder was shown a red card after he appeared to kick the youngster for withholding the ball, but the Spaniard claims both parties have admitted wrongdoing.
"Eden Hazard has been in to see the ballboy and the two have apologised to each other," Sky Sports News quotes Benitez as saying.
"The ball boy knows he was wasting time. We are disappointed to lose the player but we cannot change things. They both recognise there was a mistake.
"The boy was apologising for timewasting. Hazard was frustrated and tried to get the ball. He was kicking the ball and getting the ball."
A police investigation into the matter was opened but has since been dropped after officers spoke to the boy and his father.