Leslie passed away suddenly earlier this month at the age of 25 in what was later reported to be an apparent overdose.
Backstreet Boys star Nick performed a concert in Philadelphia and hosted a party at an Atlantic City resort on Saturday night in lieu of attending the ceremony held for Leslie in New York.
"I wanted to be at my sister's funeral, but my family has always had a complicated dynamic," Nick told The Insider in a statement.
"I love my family. I want to thank everyone for all of their compassion and support that I have received during this most difficult time. There are so many emotions for me surrounding the loss of my sister. I am trying to stay healthy, positive and focused."
Nick paid tribute to Leslie during a New York concert last week, dedicating a song to his late sister's memory.