On walls across Budapest this week, a witty opposition poster mocked how the Hungarian government wanted to take European Union handouts while opting out of the EU’s responsibility-sharing mechanism for refugees. “Hi Brussels,” the poster reads. “We still want your money.”

The quip is a reminder that while this weekend’s referendum in Hungary was born from similar frustrations to the Brexit vote in June, the Hungarian right does not want to leave the EU. Instead it wants something that is perhaps even more of a threat to the EU’s future: it wants to stay part of the union – and subvert it from the inside. Viktor Orbán, Hungary’s nationalist prime minister, seeks what he calls a counter-cultural revolution within the EU – greater autonomy for nation states and less emphasis on liberal and humanitarian principles.

While Hungary has traditionally played a minor role within European politics, Orbán’s ambitions turned him into the leading populist voice in contemporary Europe. Sunday’s referendum was his latest attempt to build political momentum for an illiberal European future – and Orbán himself presented the vote as a victory.

But analysts noted that he had ultimately failed to encourage a majority of his own population to vote against refugees and against a more humanitarian vision of the EU. As a result, this failure has arguably given some unexpected breathing space to the European politicians whose ideas Orbán so strongly opposes – notably Angela Merkel, the German chancellor, and Jean-Claude Juncker, the president of the EU commission.

“This will be viewed as a relief in Brussels,” said András Bíró-Nagy, a former EU official and the head of research at Policy Solutions, a Budapest-based thinktank. “It’s clearly a disappointing result for Orbán and I think his European ambitions will suffer as a result. In domestic politics, he’ll try to spin that he won this – but it doesn’t send a strong message to Brussels. How can he win a cultural counter-revolution in Europe if he can’t get a valid referendum result on his strongest issue in his own country?”

The impasse over the EU’s common asylum policy – the issue at the heart of the referendum – was likely to continue, Bíró-Nagy said. But his “[ideological] momentum at a European level has been stopped”.

Gerald Knaus, the head of the European Stability Initiative, a Berlin-based thinktank, said that he hoped Orbán’s setback would loosen his psychological hold over other European leaders. A prominent critic of the Hungarian leader, Knaus said members of the European People’s party, the continent’s largest alliance of centre-right parties, should now expel Orbán’s party, whose far-right policies are now at odds with mainstream Christian democracy.

“If he fails to get the necessary 50% in a referendum of his choice, where he mobilised everything he could to get people to turn up and vote – it should hopefully be seen as a sign that he is in fact vulnerable,” Knaus argued. “And that his apparent total dominance of Hungarian politics is as much about the weakness of the opposition and the strange electoral system as it is about his popularity.”

But Knaus warned that Orbán still had an outsized influence on European affairs, as indicated by “the striking indifference on the part of the EU to taking its own laws seriously”. It is still, Knaus added, “far too early – whatever the results today – to count Orbán out.”