Melbourne's dominance at the ruck was key, along with some typically resilient defence.
Jones was pleased with the Warriors' effort and application – "much better than last week" – but they were let down by some customary lapses, on both sides of the ball.
Aside from some poor defensive reads, they couldn't convert territory into enough points in the first half, then found no profit from a sustained spell early in the second half.
"The game is all about moments…we let them off the hook a few times", said Jones.
The ugly aspect of Melbourne's display was an overly aggressive approach, with several nasty first half incidents.
The worst saw Nelson Asofa-Solomona slam Wayde Egan's head into the turf with his full bodyweight, as he led with his forearm.
Egan initially feared a broken jaw (it's likely he will lose a few teeth), but the Melbourne prop surprisingly avoided the sinbin.
"It wasn't nice what happened to Wayde, because it could have been a lot worse than it was," said Jones.
Harry Grant also appeared to put his fingers in the region of Jazz Tevaga's eye in a tackle, before teammate Josh King worked him over on the ground, with both avoiding any on field sanction.
"That wasn't good either," said Jones. "His eyes are okay but it's not nice. But that's the game and we knew Melbourne were going to come with an aggressive game."
Storm coach Craig Bellamy said he hadn't seen enough of either incident and would wait for the judicial verdict.
The Warriors lost Chanel Harris-Tavita midway through the first half to a knee injury, though Wayde Egan performed well as a makeshift five eighth.
Jones said Harris-Tavita had a suspected MCL (medial cruciate ligament) injury, though scans will be needed to confirm.
He was still hopeful the 23-year-old would play again, before he quits the sport at the end of the season.
"One thing about Chanel, he will look after his injury as a real professional so I'm hoping there'll be a few more games," said Jones.
Tohu Harris was the Warriors' standout performer, with 80 minutes at prop (37 tackles, 188 metres from 22 runs) in an amazing effort.
Winger Ed Kosi also enjoyed some redemption – after his Anzac Day nightmare in Melbourne – with three tries capping a strong all round game.
Jones was also full of praise for recalled fullback Reece Walsh, saying it was one of his best performances for the Warriors. The 20-year-old constantly threatened – with eight tackle busts – and was a focal point of the attack.
"He got hands on the ball nice and early and didn't try too hard," said Jones.
Harris insisted the overall performance had given them something to build on, while both Jones and Harris were impressed by the atmosphere created by the vocal 18,395 crowd.
Bellamy was complimentary about the Warriors' display, admitting they had forced the Storm into a strong defensive effort for long periods.
"They just kept coming."
