They also beat Brisbane 2-1 in late February, when the two teams last met at Suncorp Stadium.
Buckingham and Greenacre, who took over when Ernie Merrick resigned eight weeks into the season, have since accumulated a six-win, six-draw, six-loss record. The pair have been told they'll be interviewed separately next week for the head coach role.
"Then the decision will be made as to whether that's myself, Chris, a combination or neither," Buckingham said.
Although Wellington Phoenix have finished the season on a positive note, their lack of consistency is an area Buckingham says will need to be addressed.
"The biggest noticeable thing for us this year has been especially the back-line. We've been unable to field a very similar or the same back-line for a lot of the games we've had and that's quite an important area."
However, he said there was no real need for a huge swathe of signings.
"I don't feel there is a great need - I think there are two or three real key areas that need strengthening."
Wellington have lost well-performed young defender Jacob Tratt, who has returned to Sydney, and experienced striker Shane Smeltz, who has signed with Indonesian club Pusamania Borneo FC.
Influential midfielder Roly Bonevacia, who comes off contract at the end of the season, is rumoured to be making the shift across the ditch to Western Sydney Wanderers.
"But a lot of the players that have started the last couple of games, especially, are all contracted here for next season," Buckingham said.
"With a few adjustments, this team's ready to go for next year."
-AAP