Much of the anger was aimed at leading Leave campaigner, UKIP's Nigel Farage, who was at one point accused of using "Nazi propaganda".
UK Prime Minister David Cameron is to meet European Union leaders for the first time since the UK voted to leave later on Tuesday.
He is stepping down to allow his successor to conduct exit negotiations.
Opening the session at the European Parliament, European Commission chief Jean-Claude Juncker urged the UK to clarify its position on Brexit as soon as possible.
He said he has imposed a ban on any EU commissioner talking to the British government before it formalises its intention to withdraw from the bloc.
Mr Cameron has said it will be up to the next prime minister when to trigger the formal method by which a country leaves the EU, Article 50 of the Lisbon Treaty.
In his statement to the parliament, Mr Juncker said the will of the British people must be respected, prompting applause from UK Independence Party (UKIP) leader Nigel Farage, a key campaigner behind the leave vote.
"You were fighting for the exit, the British people voted in favour of the exit. Why are you here?" Mr Junker said to him.
Others went much further. Belgian ex-PM Guy Verhofstadt, and leader of the liberal group in the European parliament, said Mr Farage had used "Nazi propaganda" in the campaign, referring to a poster showing lines of refugees.
In a veiled condemnation of Leave campaigner Boris Johnson, and likely contender to be the next British Prime Minister, Mr Verhofstadt attacked "the selfishness of one man prepared to do anything to become the prime minister of the UK".
Manfred Weber, the chairman of the European People's Party grouping, said: "The times of appeasement are over. We have to stand up for our European project."
"Apologise to the British, shame on you," he told Mr Farage, adding: "Stop this populist Brussels bashing."
Hitting back, Mr Farage told parliament that they were "in denial".
"We now offer a beacon of hope to democrats across the European continent," he said. "The UK will not be the last member state to leave the EU."
But in a speech to the German parliament, Chancellor Angela Merkel said that the EU was strong enough to survive without the UK.
She said she respected the result, but warned the bloc would not tolerate British "cherry-picking" when it came to negotiations.