The match finished 0-0, meaning victory for the Swans after they won the first leg 2-0, but the talking point was the incident involving the Belgium international and the 17-year-old ball boy.
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Hazard later apologised for the incident and Swansea have now confirmed he will face no action from the police for his behaviour.
"The police have interviewed the boy and his father and there are no charges going to be pressed, as far as they are concerned that is the matter closed,” a Swansea spokesman revealed.
"The ball boy has been into the Chelsea dressing room after the game and shaken hands with Eden Hazard. The likes of John Terry and Frank Lampard were exemplary in their behaviour in welcoming him into the dressing room.
"Chelsea asked if he could come in and our kit lady took him in and they shook hands, he is fine.
"As far as we are concerned the matter is closed. He has been a ball boy here for six years with no incidents here at the stadium."
The Blues interim manager Rafa Benitez added that the matter would be looked at by the club, and blamed Hazard's actions on frustration.
"The ball boy has been in the dressing room talking with Hazard and they have apologised to each other. They know they were wrong, that's it," he added.
"He was wasting time, Hazard was frustrated, he wanted to get the ball back quickly so they have both made a mistake and we cannot say too much.
"We will deal with this internally. We will analyse and wait to see if there is any action from the FA."