There were some bright moments in the Phoenix's first game under new head coach Darije Kalezic, featuring six new signings.
They were missing captain Andrew Durante, Tom Doyle and Michael McGlinchey who were on international duty with the All Whites in Japan this week, while Gui Finkler was ruled out with injury.
The absence of McGlinchey and Finkler was keenly felt as Adelaide won the midfield battle, looking more comfortable in possession than the hosts.
However, Alex Rufer had some excellent touches and made a brilliant run in the 32nd minute, blazing over from 20 yards out.
Before that, Phoenix defender Marco Rossi headed over from six yards out while striker Andrija Kaluderovic, struck a shoot straight at Izzo after cutting in from the left.
A mix up between Phoenix fullback Ali Abbas and Smith nearly led to a goal for Daniel Adlung.
The best second-half chance fell to Adelaide's George Blackwood but his header was denied by a reaction save from Smith.
The visitors had the better of the chances in the match, buoyed by an influential performance from Nikola Mileusnic wide on the right.
Like the Phoenix, they paid for a lack of killer touch in front of goal.
- AAP