Asofa-Solomona went off midway through the first half at Leichhardt Oval on Saturday with a suspected hamstring injury, adding another body to the Storm's casualty ward.
They faced further setbacks when fill-in hooker Bronson Garlick succumbed to back spasms and prop Alec MacDonald failed to finish the second half.
Already without Cameron Munster and Xavier Coates, and with concerns over the fitness of Ryan Papenhuyzen - who overcame a late test to play on Saturday - Bellamy's ladder-leading Storm are treading a fine line.
"I was talking to 'NAS' and he said, 'It's not that bad' ... but with all due respect 'NAS' isn't a doctor," Bellamy said of Asofa-Solomona's post-game prognosis.
"It was bad enough that he had to come off but the other guys did a good job in the middle.
"There was a lot of moving around.
"We did pretty well with our attack. I'm pretty disappointed with our defence, but having said that we only ended up with one guy on the bench."
Sua Faalogo scored two second-half tries as the Storm snuffed out a Wests Tigers comeback. (Mark Evans/AAP PHOTOS)
The win - Melbourne's fifth in a row - keeps Bellamy's men clear at the top of the ladder, but the Storm coach tipped the Tigers to be a future force after they gave his side a scare.
The Tigers were in touch at 16-12 down until the 46th minute, when Solomona Faataape was sent to the sinbin for a professional foul after taking out Storm winger Will Warbrick in the air.
Faataape's sin-binning was the 13th of the year for the Tigers, and left coach Benji Marshall frustrated his men let a chance to knock off Melbourne slip from their grasp.
"To score 28 points against the team at the top of the table, given our attack has struggled a bit this year, was good," Marshall said.
"But there were moments of frustration where we let the pressure off.
"They're first in the comp for a reason - they don't beat themselves. They showed that again tonight."
Marshall said he could see the merit in the decision of referee Peter Gough to send Faataape to the sin bin, despite the Tigers putting themselves right in the game.
Tries from Fonua Pole and Charlie Staines had kept the home side in the contest, the Storm narrowly leading after Eli Katoa, Papenhuyzen and Warbrick crossed off the back of some Jahrome Hughes brilliance.
"We wouldn't be where we are on the table if it wasn't for (Hughes)," Bellamy said.
"Ever since he's had the captaincy it seems he's gone to another level."
When Faataape went off, Hughes took control as Grant Anderson quickly extended a lead from which the Tigers never recovered.
Flyweight five-eighth Lachlan Galvin, Staines and Jahream Bula crossed to give the crowd of 10,311 something to cheer for in the second half.
But a double from Sua Faalogo and a try from the impressive utility Tyran Wishart ensured the Storm withstood a late comeback.
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