His ruling coalition retained its majority in the upper house in Sunday's vote for around the half the seats in the chamber, but fell short of securing a two-thirds majority in favour of revising the constitution.
"The hurdle of two thirds in both the lower and upper houses is extremely high," Abe told a news conference at his party headquarters.
"I want to produce a reform proposal that can be agreed upon by two thirds beyond the borders of the ruling and opposition camps," he said.
Abe has long harboured dreams of revising the constitution, which prohibits the country from waging war and maintaining a military.
But public support for revising the document is low and there is discomfort with the idea even among the ruling coalition.
Experts said that since many within Abe's coalition were already uneasy about the plans, the failure to secure a supermajority was unlikely to change the prime minister's calculations significantly.
"Losing the supermajority is not necessarily a major setback for Abe," wrote analyst Tobias Harris of the Teneo consultancy group in a note.
"Instead, by leading the ruling coalition to another national election victory -- his sixth in his nearly seven years as LDP (Liberal Democratic Party) leader -- Abe has cemented his status atop Japan's political system," Harris added.
Abe's LDP and its coalition partner Komeito took 71 of the 124 seats up for grabs in Sunday's vote, accounting for about half of the upper chamber.
The two parties already control 70 seats in the other half of the 245-seat chamber that was not being contested.
Analysts said Abe's coalition benefitted from a weak opposition, and voter turnout underscored apathy among the electorate, falling below 50 percent for the first time since a 1995 upper house election.
Abe's win is likely however to shore up his support ahead of a controversial hike of the consumption tax to 10 percent later this year, as well as trade negotiations with Washington.
The outcome of Sunday's election means Abe remains on track to become the country's longest-serving prime minister later this year.