The seventh-placed Jets missed a chance to leapfrog Sydney FC on the A-League table as two minutes of madness against Perth Glory at nib Stadium on Sunday cost them dearly.
Glory scored in the 84th and 85th minutes to steal the three points from Newcastle's grasp and dent the Jets' hopes of qualifying for their first finals series since 2010.
Zane conceded his team had to win both remaining matches against Melbourne Victory and Adelaide United to have any chance of finishing inside the top six.
"We're looking at four (points) minimum, but I think you need six (points) to make the six and one thing that's positive is we've got two home matches and we've won our last two at home," Zane said.
“I've said to the boys to dust themselves off… it was a close one today and not a great performance, but I think we're getting closer to becoming a team that can pick up points when we don't perform to the level that we'd like.
“I hope we can put in two very solid performances in front of the home fans and really give the top six a shake."
Newcastle will be without midfielder Zenon Caravella for the rest of the season after he strained a medial ligament in his left knee early in Sunday's match.
Caravella had established himself in the team during teammate Ben Kantarovski's long absence through injury earlier this season.
Kantarovski replaced Caravella after 17 minutes and looms as his likely replacement in the starting side against Victory.
"Zenon had a good back half of the season, so from a personal point it's not great that he's injured because he was doing such a good job for us, but I believe in the ones on the outside to carry on where Zenon's left off," Zane said.
"Kanta is probably suited to start rather than come off the bench, so it's a pretty obvious straight swap there and I'm not too concerned because I think he can do an equal job to Zenon."
One positive for the Jets was Adam Taggart's 14th goal of the season all but securing the prestigious Golden Boot award.
However, Zane was reluctant to put any extra pressure of the young striker, who is three goals clear of Brisbane Roar's Besart Berisha, Melbourne Heart's David Williams and Melbourne Victory's James Troisi.
"There's still going to be pressure on him from behind, but he doesn't need to look at that anymore," Zane said.
"He's got two big games and we don't want to put all the pressure on the young kid, but hopefully he can add a few more before the season ends and give us a glimmer of hope that we can still make that top six."
