Liberal Premier Jeremy Rockcliff claimed victory at the election on Saturday, with his party securing 14 seats compared to Labor's nine.
But both major parties have fallen short of the 18 needed for a majority, with negotiations set to begin on forming a minority government.
Party members should be hopeful about the future of the federal division, despite its election wipeout in May, Deputy Liberal leader Ted O'Brien said.
"There's clearly a difference between federal and state elections, but those who think the Liberal Party is on its knees and nearly dead, I think you can only just look at the Tasmanian election," he told Sky News on Sunday.
"We are rebuilding, and so, if anything, it really should be a message of inspiration to Liberals right across the country.
"Hopefully sanity will prevail. I don't think Tasmania deserves yet more uncertainty over the weeks ahead."
Saturday's election was the fourth time in seven years voters in the state have headed to the polls.
Former federal Liberal MPs who were defeated at May's federal election have been voted into the state's lower house, including Bridget Archer and Gavin Pearce.
Tasmanian Liberal senator Jonathon Duniam said there were many reasons why the party did not perform at the federal election but had the largest vote share at the state poll just two months later.
"We ran a bad (federal) campaign. We didn't run a campaign relevant to Tasmania. We weren't speaking to their issues," he told ABC's Insiders program.
"Politics is local, and never has that been more true than in a place like Tasmania. They own their politicians, they own their issues. They want Tasmanian solutions."
While Liberal and Labor parties in Tasmania were in negotiations with the crossbench to form minority government, Senator Duniam said there was not a conceivable path for Labor to get into power.
"It would be an unimaginable disaster for there to be a Labor party that's gone backward in the polls to join up with the Greens and a range of crossbenchers who have all very disparate views about the future of our state," he said.
"It would send us backward, and we'd be back at the polls in no time."
Labor experienced its worst-ever result at a state election, receiving just 26 per cent of the primary vote.
Labor frontbencher Michelle Rowland said time was needed to work out the results in the state.
She said the result was likely Tasmanians backing the status quo.
"There is something to be said about the desire for stability, I think, by all voters," she told Sky News.
"This has a bit of a way to go in terms of the count and in terms of who may be in a position to form what looks like minority government."
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