The defendant began communicating with the teenager on Facebook in May.
Within days she had told McKenzie how old she was, in response to his specific requests, court documents stated.
"Despite knowing her age, the defendant continued to send her sexualised messages and also invited her to visit him at his flat," a police summary said.
On May 21, the victim went to McKenzie's home.
The pair watched a movie before their brief romance was consummated.
"Soon after, the victim phoned police," Judge John Macdonald said.
"Clearly she was uncomfortable about what happened."
A victim impact statement written by the girl's parents said she was "unable to cope" with the situation.
"Her parents are quite devastated by what happened," the judge said.
The court heard the victim had since exhibited mood swings, had trouble sleeping and was finding school difficult.
McKenzie's attitude was originally assessed as "blase" after he was interviewed by Probation, but counsel Jim Takas said a letter written by his client contradicted that.
"He's taken a good, hard look at himself," Takas said.
The judge accepted the defendant was truly remorseful and had shown insight into his offending.
McKenzie's sex crime came while he was on bail for stealing cash during his work as a cleaner.
For that he was sentenced to community detention, community work and supervision.
Judge Macdonald cancelled that sentence apart from the 146 hours of community work that would remain.
Because of the nature of the charge, McKenzie could have been added to the Child Sex Offender Register.
But Crown prosecutor Richard Smith did not press the issue "given the circumstances of the offending".
