The men's tour said it conducted a full investigation and that all available evidence was reviewed, including match footage and interviews with match officials and other tournament personnel who were in close proximity to the players.
"Unfortunately, the audio recording on the match footage did not pick up verbal exchanges between the players," the ATP said in a statement.
"At this time no evidence has been found to support the allegation that Ryan Harrison used a racial slur during the match."
Following his defeat world number 65 Young took to Twitter to offer his views on what had happened.
"I'm shocked and disappointed, Ryan Harrison, to hear you tell me how you really feel about me as a black tennis player in the middle of our NY match," Young said. "I thought this was supposed to be an inclusive gentleman's sport."
Young did not elaborate on what was actually said between the pair, but world number 44 Harrison was quick to respond.
"The accusations made by Donald Young tonight following our match are absolutely untrue," said Harrison.
"I'm extremely disappointed that someone would say this in reaction to a lost tennis match. Any video/audio will 100 percent clear me and I encourage anyone with the available resources to find it."
(Reporting by Frank Pingue in Toronto; Editing by Toby Davis)
