The former UKIP leader later said that "gangsters" was a more appropriate word.
Nigel Farage has been jeered in Strasbourg after comparing the EU Parliament to the Mafia over its Brexit demands.
Asked to retract his "unacceptable" remark by the body's president, Italian Antonio Tajani, the former UKIP leader agreed - saying "gangsters" was a more appropriate word.
It became even more heated when Guy Verhofstadt, the EU Parliament's Brexit coordinator, said he expected the UK to rejoin the EU when the next generation "see Brexit for what it really is: a catfight in the Conservative party that got out of hand, a loss of time, a waste of energy, stupidity".
The row broke out as MEPs laid down their red lines for Brexit negotiations, voting by a margin of 516 to 133 (50 abstentions) in favour of agreeing the terms of the divorce first before striking a new trade deal with the UK.
Mr Farage told the gathering in Strasbourg: "Already you have made a series of demands that are not just unreasonable but in some cases clearly impossible for Britain to comply with.
"You began by telling us that we have to pay a bill - a cool £52bn sterling - a figure that has clearly been plucked out of the air, effectively a form of ransom demand... really, you should be making us an offer we can't refuse to go.
"You have shown yourself with these demands to be vindictive, to be nasty. All I can say is, thank goodness we're leaving.
"You are behaving like the Mafia. You think we are a hostage. We are not, we are free to go."
Mr Farage warned against forcing the UK to walk away from the talks with no deal: "You know we don't have to buy German cars, we don't have to drink French wine, we don't have to eat Belgian chocolate. There are a lot of other people who will give that to us."
He said a return to tariffs would put hundreds of thousands of jobs at risk within the EU.
Mr Farage also took a swipe at European Council president Donald Tusk.
Noting his absence, he said: "I suspect that he is still crying. He looked pretty tearful, didn't he, after the British ambassador delivered the letter?"
Speaking later, the former UKIP leader said the EU "needs to give some ground otherwise there simply cannot be a deal of any kind."
He told Sky News: "Maybe if they had asked for £5bn or £10bn we could have sat down and had some negotiation.
"It is a ludicrous figure and you cannot negotiate on that basis".