Luke Jovanovic almost found the net inside 30 seconds on Friday, but after a dominant first half from Adelaide, Phoenix broke the deadlock on 35 minutes thanks to Manjrekar James who got the last touch off Corban Piper's header.
After a host of chances, Jovanovic finally hit the target with a brilliant individual effort on 55 minutes, but for all of the Reds' bluster, Wellington's resilient performance was enough to keep United at bay and earn them a share of the spoils.
Andrioli admitted he was expecting such a display from the visitors who were in bottom place heading into the clash and two games into Chris Greenacre's fourth spell as interim coach of the Phoenix.
"One hundred percent, I knew this was going to be a difficult game," he said.
"We knew they were going to play this type of game and I guess what didn't work out for us was we should have scored after 40 seconds.
"Then we concede against them, and they want to defend deep in the block and play in transitions and they've got big boys in the box."
In three matches this season, the Reds have failed to beat Wellington. In the previous two encounters in New Zealand, the two sides played out a 2-2 draw in January following a 2-1 win for the Phoenix in November.
Andrioli, who congratulated Ryan Kitto after his 250th match for the Reds, holds Wellington in high regard despite their lowly position on the table, the draw temporarily lifting Phoenix above Western Sydney Wanderers ahead of their clash against league leaders Newcastle later in the round.
"The reason why we couldn't beat them I can't put my finger on it but it's behind us now. We played another game and haven't lost; wanted the three points, so now we just have to regroup and go again next week," said Andrioli.
Greenacre was full of praise for his side. The point was his first since taking the reins a fortnight ago after Giancarlo Italiano stepped down after a 5-0 home loss to bitter rivals Auckland FC.
Greenacre's first match in charge was a 1-0 loss to Sydney at home last week, but this time he insisted: "My players were like warriors tonight."
