The Christian Social Union (CSU), the sister party of Merkel's own Christian Democrats (CDU), slumped to its worst result in almost 70 years in Sunday's election in Bavaria. The chancellor's other coalition partner, the centre-left Social Democrats (SPD), saw its support halved, Reuters reported.
"My lesson from this is that I, as chancellor, must make sure that trust is won back. I will work on that with as much vigor as I can," she said at an event of the BGA trade body.
CSU leader Horst Seehofer, who is also interior minister in Merkel's loveless coalition, had hoped his anti-immigration rhetoric and criticism of Merkel's liberal asylum policies would help his party fend off a threat from the far-right in Bavaria.
His strategy backfired as the CSU, which has ruled Bavaria for almost six decades, bled votes to the far-right Alternative for Germany (AfD) party and the ecologist Greens in equal measure. On Monday, he appeared to extend an olive branch.
"We will do our bit to ensure that the coalition can continue to do its work in a stable manner despite some of the comments that were made yesterday," Seehofer told reporters.
He was referring to angry CSU delegates who blamed their party's dismal showing on Merkel's decision in 2015 to welcome some one million, mainly Muslim, asylum seekers, which has fueled the rise of the AfD.
Merkel said the CSU had lost its absolute majority in the Bavarian parliament even though the regional economy was doing well.
"This shows that even a good economic situation and almost full employment are not sufficient if trust is lacking," Merkel said.
The Bavarian economy grew by 2.8 percent last year, outpacing the national rate of 2.2 percent. It also has the lowest unemployment rate in Germany, 2.8 percent, compared with just over 5 percent nationally.
The AfD gleefully seized on the election outcome as a sign of a broader malaise for Merkel's coalition, which has been shaken by disputes, including over immigration, since it took power seven months ago.
"We are very pleased because the goal for the Bavaria state election was to send an earthquake towards Berlin," Martin Sichert, AfD leader in Bavaria, told a news conference. "This earthquake happened .... We are now excited to see what the consequences will be here in Berlin."
The CSU also lost support to the Free Voters, a protest party of mainly conservative independents.
In Bavaria, the CSU will now try to form a coalition either with the Free Voters - its preferred option - or with the Greens who are ideologically distant.