• Pressure is mounting within the CDU-CSU after preliminary final election results published Monday showed that the center-right bloc narrowly lost to the center-left Social Democrats.
• The election results make a coalition government necessary, and it's looking increasingly likely that the CDU-CSU may be heading into opposition.
• The CDU-CSU's candidate for chancellor, Armin Laschet, has insisted that the bloc has a mandate to govern.

The reckoning has already begun for outgoing Chancellor Angela Merkel's conservative alliance, a day after election results pointed to its worst-ever showing since its formation at the end of World War II.

Pressure is mounting within the Christian Democratic Union-Christian Social Union bloc after preliminary results published Monday showed that the center-right alliance achieved 24.1% of the vote, compared with 25.7% for the center-left Social Democratic Party.

The results make a coalition government necessary, and it's looking increasingly likely that the CDU-CSU may be heading into opposition, although its candidate for chancellor, Armin Laschet, insists that the bloc has a mandate to govern with less than a quarter of the vote.

Having essentially ruled out forming another so-called "grand coalition," the SPD and CDU-CSU are preparing to court two smaller parties — the Greens and the pro-business Free Democrats — with the aim of enticing them into a governing alliance.

The Greens and FDP, who are now effectively in the position of kingmakers, look set to discuss their respective positions together this week before engaging with the larger parties.

Despite acknowledging that his party had fallen short of expectations, Laschet said Monday he was optimistic about forming a coalition.

"There is no question that this result cannot, must not and will not satisfy the Union. We managed to catch up in the final spurt and prevented red-red-green, but at the same time there are painful losses. It was not enough for first place," he told party members.

Despite Laschet's optimism, the soul-searching has already begun in Merkel's CDU party with a clamor growing for Laschet to resign, German media reported Tuesday.

Criticism of Laschet had grown overnight, the Bild newspaper reported Tuesday, with leading CDU officials saying the party should accept the will of the voters and concede victory to the SPD. There are rumblings in the German media that pressure could be exerted on Laschet to stand down.

The newspaper quoted Lower Saxony's CDU boss Bernd Althusmann as saying that "we should now humbly and respectfully accept the will of the voters, with decency and attitude. Change was wanted."

Hesse Prime Minister Volker Bouffier said the CDU-CSU has "no claim to government responsibility" while Tilman Kuban, head of Junge Union (the young wing of the CDU-CSU), was quoted as saying "we lost the election. Period. The clear mandate lies with the SPD, Greens and FDP."

Adding insult to injury, the Bild newspaper reported a survey by polling institute Forsa on Tuesday suggesting that the CDU-CSU union could have achieved 30% of the vote if CSU head Markus Soeder had been the bloc's candidate for chancellor instead of Laschet.

The electorate seems to agree that Laschet should not claim a mandate to govern, with most Germans opposing the prospect of another conservative-led government after Merkel's nearly 16 years as chancellor.

According to an opinion poll by the Civey institute for the Augsburger Allgemeine daily, 71% of over 5,000 respondents oppose Laschet trying to become chancellor after the party's poor performance. The poll, conducted Sunday and Monday, found that only 22% of Germans supported Laschet's claim to have a mandate to form a government.

A bad trend

The latest blow for the CDU cannot all be blamed on Laschet as the decline in the CDU's share of the vote continues a trend seen in the last couple of elections.

Still, the election came at a time of vulnerability for the conservatives ahead of Merkel's departure.

Excluding the CSU's results, the CDU achieved just 18.9% of the vote, down 7.9 percentage points from the 2017 vote. Conversely, the SPD has seen its share of the vote rise 5.2 percentage points since 2017, as did the Greens and Free Democrats, official data from the Federal Returning Officer show.

Jeffrey Rathke, president of the American Institute for Contemporary German Studies, told CNBC Tuesday that while it was important not to write Laschet off just yet "all the bets now are on the Greens and the FDP trying to find a way to work with Olaf Scholz and the Social Democrats."

Marco Willner, head of Investment Strategy of NN Investment Partners, said coalition talks won't have a fast outcome.

"It's a very strange situation at the moment where really, for the first time, the small, junior partners in this coalition set the tone and are looking to choose the senior partner in this game. Clearly the SPD have the lead here, but it's day two after the elections and I expect this to go on for some time and who knows down the road where this will lead to," he told CNBC's "Squawk Box Europe" Tuesday.

Why did the CDU do so badly?

There are several reasons why Merkel's party is judged to have fared badly in this latest election, including the rise of a younger, more environmentally conscious electorate and an increasing number of voters who want to see Germany invest in itself and modernize its infrastructure, be it in the industrial, digital or transport sectors.

"What's required economically is significant change," Clemens Fuest, president of Germany's Ifo Institute, told CNBC on Tuesday. "We are facing challenges like climate change and digitization, so the challenge will be to have a three-party coalition that has to compromise a lot."

Another of the reasons the party has fared worse in this vote is undoubtedly due to the imminent departure of Merkel. Experts note that previous votes for the CDU-CSU bloc were in fact votes for Merkel, a trusted leader who attracted voters for her pragmatic and steady approach to politics at home and abroad.

Despite attempts to make Laschet appeal to voters as a continuity candidate and someone who can fill Merkel's shoes, he has not had the same appeal, and has even managed to alienate many during the election campaign, having been caught on camera laughing during a visit to a flood-hit German town.  

Read more: Without Merkel, many German voters don't know who to vote for

For some, Laschet's biggest disadvantage was that he simply wasn't as likable a candidate as his main rival, Scholz, and that he just simply isn't Merkel.

Matthew Oxenford, Europe analyst at the Economist Intelligence Unit, noted simply that "Scholz proved a much more compelling chancellor candidate than the CDU/CSU's Armin Laschet."

Thomas Gschwend, a professor at the Department of Political Science at the University of Mannheim, told CNBC ahead of the vote that "the CDU tried to stage their campaign that Laschet was a natural successor of Merkel, but people just didn't buy this story because he's not Merkel, he's not like her."