The Auckland-based outfit were outclassed in atrocious conditions at Mount Smart Stadium, despite putting up a solid showing through the middle of the park.
No side dominated the rain-soaked tussle, but the Storm proved too ruthless in their execution, nabbing four tries to two and grinding out the two points.
Kearney was pleased with his forward pack's showing but rued the team's inability to see out the 80 minutes after losing Roger Tuivasa-Sheck to concussion.
Halves Shaun Johnson and Ata Hingano failed to make the most of their fifth- tackle options, while Cooper Cronk put on a clinic as Melbourne's No.7.
The Queensland playmaker scored a try and laid on two more for his side as they continued their perfect start to the season.
"They're a benchmark of the competition," Kearney said.
"The way they play, they don't give you a great deal - you've got to really make sure you're executing and I just didn't think we did that.
"We put ourselves right in the contest for most of the game (but) we just let it get away from us at the back end."
AAP reports the Warriors struggled early for the second consecutive week in Auckland, allowing Melbourne to dominate.
Last year's grand finalists scored with their first genuine attack in the seventh minute through Kenny Bromwich, before having another ruled out three minutes later.
The disallowed try appeared to stir the Warriors who scored two quick tries through Tui Lolohea and Johnson.
But an unfortunate Lolohea slip seconds from halftime gifted Cheyse Blair a four-pointer and set the tone for the second stanza.
Suliasi Vunivalu scored early after the break as the Warriors attempted to adjust without Tuivasa-Sheck, before Cronk closed out the contest.
"Our guys gritted their teeth and just kept making their tackles, turning up, so I think we got the result we probably deserved," Storm coach Craig Bellamy said.
"It's tough in those conditions, the amount of rain we've had, how slippery the ball's been.
"The conditions tonight weren't conducive to the way they wanted to play, and I know it wasn't for us either, so it ended up a bit of a grind."
The Storm can look ahead to next week's tussle with Brisbane, while the Warriors - boosted by the expected return of Kieran Foran - will play Canterbury.
Kearney expected skipper Tuivasa-Sheck to be fine for the encounter in Dunedin, having quickly come to his senses after his head knock.
He will have to go through concussion protocols throughout the week.