Scott spoke about the break-up while attending a personal appearance at 1OAK Nightclub in Las Vegas on Friday (24 July).
According to Us Weekly, Scott told reporters: "[I'm] just taking it one day at a time. With everything going on right now, I need to be positive for myself."
Scott, 32, wore a grey suit and white shirt for the club night, and eyewitness accounts told the US publication that he appeared "restrained".
News of Scott and Kourtney's split emerged earlier this month, with reports suggesting Kourtney ended their relationship due to Scott's excessive partying following pictures of him hanging out with another female.
Last week, Scott was pictured meeting up with Kourtney and the couple's three-year-old daughter Penelope at the Beverly Hills Hotel.
Scott and Kourtney are also parents to five-year-old son Mason and seven-month-old son, Reign.
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All you need to know about Kourtney Kardashian: