The Jets scored three goals in eight minutes to leap from last to eighth on the A-League Men table.
Eli Adams and Lachie Rose scored in the 50th and 54th minutes, then Clayton Taylor added a third in the 57th at Sky Stadium on Sunday.
Ifeanyi Eze got a goal back in the 76th minute, but it proved too little too late in an action-packed clash where Jets goalkeeper James Delianov (seven saves) also starred.
Italiano lamented injury-hit Wellington's defending in his Sky Sports interview, then doubled down in his press conference.
"It's just unacceptable losing 3-1 at home like that," he said.
"It leaves a bitter taste in my mouth and I think if this group is going to do anything, it needs to mature very, very quickly because we're running out of games now and that was a big three points for us, especially at home."
In a desperately close table, Mark Milligan's Newcastle (nine points) are now only outside the top six on goal difference, while Italiano's Wellington (eight points) sit 11th, only ahead of Melbourne Victory.
"This game can be ruthless in terms of you don't always - in fact, you very rarely - get what you deserve," Milligan said.
"You have to go and earn everything that you get in this game, and I felt today they did that."
There was carnage in the second minute on Sunday when Max Burgess hit the deck, grabbing at his right groin.
Jets playmaker Burgess attempted to continue but had to be substituted for Adams in the fifth minute.
"It's just a groin strain. Not sure really of the severity yet. He'll get scans when we get back to Newcastle," Milligan said.
The superb Delianov and counterpart Joshua Oluwayemi were both busy in a high-octane first half full of chances for both teams.
The Jets finally broke through when Will Dobson released Taylor.
The attacker stood up Matthew Sheridan and cut the ball back to Alexander Badolato, who found Adams, with the winger's deflected shot beating Oluwayemi.
Eze had a golden opportunity to equalise blocked and Newcastle pounced again.
The Jets caught Oluwayemi off his line with a Kosta Grozos long ball. The goalkeeper attempted to intervene and Rose pounced, nipping in front of the Phoenix goalkeeper before shooting into an empty net.
Newcastle effectively sealed all three points when Taylor played the ball out wide to Daniel Wilmering, then burst forward to receive it back and score.
Eze gave Wellington a lifeline when substitute Fin Roa Conchie lifted a lovely ball towards the striker, who scored with a terrific looping header, but it proved too little too late.
Newcastle return home to host Sydney FC next Saturday.
Wellington host Central Coast on Saturday, seeking to avoid a third straight defeat.
