BERLIN — Chancellor Angela Merkel’s conservative bloc lost its grip on the upper house of Germany’s Parliament on Sunday, as voters in an important regional election dealt her party a strong setback seen as the first significant political fallout from the Greece crisis.

A wide majority of Germans had opposed bailing out the heavily indebted Greek government, but Mrs. Merkel pushed Germany’s part of the $140 billion rescue package through Parliament last week.

Mrs. Merkel’s effort had been expected to cost her Christian Democrats in the regional election in North Rhine-Westphalia, Germany’s most populous state, but the steep drop of 10 percentage points compared with the last election, in 2005, was even larger than most analysts had predicted and gave the Christian Democrats their worst postwar showing in that state.

The loss means Mrs. Merkel can no longer count on a majority for her governing coalition in the upper house of Parliament, composed of delegations from all 16 states. “This is a debacle for the government,” said Peter Lösche, emeritus professor of politics at the University of Göttingen.