The result leaves the Warriors in eighth spot on the premiership ladder while Melbourne's seventh straight win saw the reigning premiers claim top spot above the Dragons and Rabbitohs.
Coach Stephen Kearney was satisfied with the attitude and effort from his players but lamented their inability to convert scoring chances.
"There was some really courageous effort and energy out there but it was one of those games you'd classify as a missed opportunity," said Kearney.
"We just didn't quite execute well enough and when you're playing a side like Melbourne it comes down to those moments."
The Warriors were dealt a blow with Luke hampered by a recurring calf injury though the first half before he was eventually forced off in the 51st minute.
Kearney was optimistic the Kiwi international would recover in time for next Sunday's away game against the Titans.
"[Luke's] had a bit of an issue with it over the last couple of weeks so we'll monitor it and see how he goes and get him rested and worked on and get him right for next week," he said.
However, lock Adam Blair may find himself in hot water with the NRL's match review committee after he was placed on report for a late and high tackle on Storm fullback Billy Slater.
The Storm got off to a hot start with Chambers scoring in the third minute but the Warriors hit back quickly through Beale and halfback Shaun Johnson's conversion provided a narrow lead.
Errors saw them unable to get to their kicks on two sets while poor execution saw scoring chances missed, before Vunivalu claimed a chip-kick to give Melbourne the lead just before halftime.
A double movement saw Warriors centre Solomone Kata denied a try early in the second half and the gamble of a short drop-out cost them with the ball going out on the full and the resulting penalty allowing Smith to extend his side's lead.
The Warriors pushed hard inside the dying stages but an offside penalty against Simon Mannering saw Smith have the final say with his second goal in the 77th minute.
Warriors captain Roger Tuivasa-Sheck praised the work of Johnson and fill-in five-eighth Mason Lino while shouldering the blame for costly errors down both flanks.
"They both played really well. Shaun took ownership of leading the boys around and he did a really good job," said Tuivasa-Sheck.
"I put my hand up for a few missed opportunities where we had our shape up nicely.
"I'm pretty disappointed in those so that's the lesson we'll take out of tonight."
Storm 12 (Will Chambers, Suliasi Vunivalu tries; Cameron Smith 2 pens)
Warriors 6 (Gerard Beale try; Shaun Johnson 1 con)
