Justice Minister Stephanie Vallee and Jean-Marc Fournier, who is responsible for Canadian intergovernmental affairs, hailed the decision as "historic" but said the new Liberal government is more interested in focusing on bread-and-butter issues.
"The question is, 'what are your priorities?'" Fournier told a news conference in Quebec City.
"It is the economy. If you're asking whether it is 250,000 jobs or 24 Senate positions, it's the 250,000 jobs."
Fournier was referring to a Liberal promise in the recent election campaign to create 250,000 jobs over five years.
Both ministers said Quebec would be an active participant in any future talks about reforming the Senate but that the province would want to discuss other constitutional issues such as immigration, the distinct-society clause and the appointment of Supreme Court justices.
Liberal Leader Philippe Couillard, who is now premier, mused during the election campaign about travelling to the rest of the country to discuss the idea of eventually holding talks aimed at getting Quebec to sign the Constitution.
After being accused by his political rivals of wanting that signature at any cost, Couillard backtracked and said there was little appetite at the moment for constitutional negotiations.
The Supreme Court ruling said Senate reforms would require constitutional amendments approved by at least seven provinces representing 50 per cent of the population.
The judgment also said abolishing the Senate would require the unanimous consent of all 10 provinces.
Vallee called the ruling "historic."
"Since 1982, there had never been a decision that specified how Senate reform could be achieved," she said.
Fournier said recent Supreme Court decisions have reaffirmed the "inescapable" role of provinces in shaping the future of major institutions such as the Senate.
"For the Quebec government, federal institutions are at the heart of Canadian federalism," he said.
"These institutions do not belong to the federal government or the federal Parliament. The Supreme Court agrees with us."
The Parti Quebecois, meanwhile, pointed to the ruling as further evidence that federalists are stuck in a country whose institutions cannot be reformed.
"Everyone is aware that there is a problem with federal institutions, that Canada is caught in this kind of straitjacket," said Alexandre Cloutier, who was intergovernmental affairs minister until the PQ's election defeat.
"They're caught in these old institutions and with senators who don't respect their role."