Angela Merkel has taken responsibility for her party’s disastrous showing in Sunday’s Berlin state election, admitting mistakes in her handling of last year’s refugee crisis.

In an unusually self-critical but also combative speech, the German chancellor said on Monday afternoon she was fighting to make sure there would be no repetition of last year’s chaotic scenes on Germany’s borders, when “for some time, we didn’t have enough control”. “No one wants a repeat of last year’s situation, including me,” Merkel said.

However, she did not distance herself from her decision last September to keep open Germany’s borders to thousands of refugees stranded at Keleti station in Budapest. The mistake, the chancellor said, was that she and her government had not been quicker to prepare for the mass movement of people triggered by conflicts in the Middle East.

“If I was able to, I would turn back time by many, many years, so that I could have prepared the whole government and the authorities for the situation which hit us out of the blue in the late summer of 2015,” she said.

Sunday’s election ushered in a new era of multi-party politics for the German capital, with the two governing establishment parties, the Christian Democratic Union (CDU) and the Social Democratic party (SPD) plummeting to the worst Berlin result in their parties’ histories, while the leftwing Die Linke and anti-immigrant Alternative für Deutschland (AfD) enjoyed impressive gains.

On Monday, Merkel admitted she had failed to sufficiently explain her refugee policy, and that her phrase “Wir schaffen das” (“We will manage”) had provoked some of those who did not agree with her political course. Her words will be interpreted as an olive branch to the leader of her CDU’s sister party, the Bavarian Christian Social Union (CSU), who has repeatedly called on her to distance herself from the much-cited slogan.

For too long, Merkel said, she had relied on procedure according to the Dublin resolution, “which, to put it simply, had taken the problem off Germany’s hands”, adding: “And that was not good.”

Facebook Twitter Pinterest Georg Pazderski, the Berlin leader of Alternative für Deutschland. The anti-immigration party made strong progress in suburbs in the formerly communist east. Photograph: Axel Schmidt/Reuters

Merkel, 62, also rebutted the CSU’s calls for a “static upper limit” to the amount of asylum seekers Germany could accept in 2016, arguing that it “would not solve the problem”. Banning people from entering the country on the basis of their religion, she said, would be incompatible with Germany’s constitution and her own party’s “ethical foundations”.

She lamented that the European Union as a whole was failing to recognise the refugee crisis as “a global and a moral challenge”. “What we are seeing in Europe is a realisation that we are no longer leading the field when it comes to globalisation, we are not setting the pace.

“In 1990, when the wall fell, the cold war came to an end and freedom blossomed everywhere; it looked like we were on an irreversible road to victory, and that it was just up to the rest of the world to join our model. Freedom had won. It now turns out things aren’t that simple”.

Sunday’s result served to illustrate the extent to which party political landscapes across Europe are becoming ever more fractured. The Social Democrats had unwittingly hit the nail on the head when predicting in their poster campaign that “Berlin will stay multifaceted”.

AfD’s Berlin leader, Georg Pazderski, on Monday hailed his party as “the biggest democratic project of the last few decades” after it entered its 10th state parliament in a row. The AfD had managed to mobilise 64,000 “non-voters”, as opposed to 41,000 “non-voters” who gave their support to all the other parties put together.

Henrik Enderlein (@henrikenderlein) Schaut auf diese Stadt.

Reicher Rand West: CDU

Armer Rand Ost: AfD

Urban West SPD

Urban Ost: Linke

Gentrified: Grün pic.twitter.com/irmFWElbFj

The fledgling party profited most in the suburbs in the formerly communist east, such as Treptow-Köpenick (with 20% of the vote), Lichtenberg (30%), and Marzahn-Hellersdorf (23.2%), areas in which many lower-income residents have been considerably affected by rising living costs, and where many were outraged when refugee accommodation was built without them being consulted.

The AfD also secured 12.2% in the adjacent working-class district of former west Berlin, Neukölln, where many long-term residents accuse the longstanding SPD leaders of insufficiently protecting the district’s residents and actively supporting gentrification.

But it was in Pankow – a district in the north of Berlin which includes the trendy, gentrified Prenzlauer Berg area – that the AfD’s performance was most surprising, as it got more votes (13.8%) than the CDU (12.6%).

The CDU, which fell back to its worst result since the end of the second world war, unsurprisingly received its strongest support in the well-off suburbs to the west, such as Reinickendorf and Steglitz-Zehlendorf, where the party has always had a solid support base. Its general secretary, Peter Tauber, argued the party had not had enough time in office to make up for a decade of mismanagement from when the SPD and Linke had ruled the city.

Facebook Twitter Pinterest Berlin’s Brandenburg airport, which was meant to open in 2012 but is still unfinished. The botched project was one of the issues debated during the election. Photograph: Fabrizio Bensch/Reuters

The urban centre to the west was where the SPD emerged as the clear winner, albeit with losses of 7%, while Die Linke did best in the urban centre to the east, where it recovered from losses endured five years ago.

The Greens received the majority of their votes in the most gentrified parts of the city, as did the pro-business Free Democrats (FDP), the main thrust of whose campaign was to keep open Berlin’s Tegel airport.

From disputes over how to deal with the city’s dog waste, to rising rents, to the city authorities’ inability to process refugee applications, or the failure after years of waiting to get Berlin’s new airport off the ground – it is still a building site costing Berlin taxpayers €1m a day – the challenges facing the city that were fleshed out during the election campaign are many and varied.

Most agree that this government will be crucial in deciding Berlin’s future and whether it will continue to be a popular and open place to live or “suffocate under its own success”, as Berliner Zeitung newspaper put it.