The well-travelled Englishman stepped up to the head coach`s position after Ricki Herbert resigned on Tuesday, but was unable to have an immediate impact.
Adam Taggart put the Jets ahead after 19 minutes and when Michael Bridges scored just before the break, the game was up.
Jeremy Brockie pulled one back on the hour mark but it was not enough to get the Phoenix off the bottom and they remain a point behind Perth.
Herbert, who remains the manager of the New Zealand national team, ended his six-year stay with the Phoenix on Tuesday.
"I've had a long and very successful tenure at the club and will always be proud of what I have achieved," he said.
"But all good things must come to an end and it's time for new coaching blood and for me to move on to new and exciting challenges"
Thirty-five-year-old Greenacre, who started his career with Manchester City, has taken the job until the end of the season on an interim basis.
His most successful spell as a player came with Mansfield for whom he scored 58 goals in 134 appearances and, after a similarly rich time with Tranmere, joined Wellington as a player in 2009.