Hazard was shown a red card deep into the second half of the 0-0 draw at the Liberty Stadium, after he showed his frustration when the ballboy refused to return the ball to the Belgian.
The youngster was helped away from the pitch as he winced in pain after receiving a boot to the ribcage area, but Benitez said both parties resolved their differences in a meeting that took place in the changing rooms after the match.
"I didn't see the incident from the bench, but afterwards the boy came in to talk to Hazard, and both apologised to each other," Benitez told Sky Sports.
"The boy knows he was wasting time, Hazard was frustrated because he wanted to get the ball back. They apologised, they made a mistake, and that's it.
"We're disappointed because we lost a player but the best thing is to move forward."
South Wales Police will not investigate the incident after the youngster said he would not press charges.
In a statement Chief Superintendent Josh Jones, of South Wales Police, said: "South Wales is aware of the incident involving a ballboy at the Liberty Stadium in Swansea. We are making arrangements for him to be interviewed. South Wales Police takes such matters very seriously.''
However, the ballboy met with police at the stadium and revealed that he would not be taking any further action.
Reflecting on Chelsea's dire performance, which saw them barely threaten despite needing to score twice to rescue the tie, Benitez said the damage was done in the first leg.
"We didn't take our chances in the first leg, and we didn't take our chances in this leg. Credit to Swansea," he said.
The Chelsea boss also refused to blame referee Chris Foy, who turned down a first-half penalty appeal when Demba Ba went down in the area, saying: "It does not matter, we cannot change this. We didn't take our chances."
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