The 23-year-old brushed off concerns over a knock to his quad and while disappointed with the result, was happy with his side's first-half showing.
"I was happy with the way I went," said Tuivasa-Sheck.
"Just to get a run and lead out the team was good for me. It's been so long since I was on the field I was just excited for the game.
"The Storm's experience picked up and they rolled through our middle and a few of our young boys couldn't handle them.
"I pulled up well. I was more worried about my lungs. That (ice) was for my quad, just a bit of a cork and precautionary."
Halfback Shaun Johnson showed no ill-effects of the groin strain that sidelined him at last week's NRL Auckland Nines.
The Kiwis international defended strongly and delivered passes for their first two tries to forward Bunty Afoa and wing Tui Lolohea, before a banana-like kick found Tuivasa-Sheck to claim and score beside the posts.
The Warriors momentum came off the back of some good go-forward, with front-rower Charlie Gubb strong and 18-year-old lock Isaiah Papalii filling in well for former skipper Simon Mannering.
With Tuivasa-Sheck, Johnson, Ryan Hoffman, Solomone Kata, David Fusitu'a and Albert Vete all rested after the break, the Storm worked a second try through Slade Griffin, before late four-pointers to Jeremy Hawkins, Linc Port and Young Tonumaipea gave them the win.
"There were some good signs particularly in the first-half," said Kearney.
"I don't like getting beaten at the best of times, but the Storm were strong in the basics and fundamentals and it was a good lesson for us in the second-half."
Melbourne Storm 30 (Joe Stimson, Slade Griffin, Jeremy Hawkins, Linc Port, Young Tonumaipea tries; Cameron Munster con; Scott Drinkwater con; Dylan Kelly 3 cons).
Warriors 18 (Tuimoala Lolohea, Bunty Afoa, Roger Tuivasa-Sheck tries; Mason Lino 2 cons; Ata Hingano con).
Halftime: 18-6 Warriors.