In a frank briefing, Anthony Gardner made a staunch defence of the EU and warned of the "dangers" of a hard Brexit.
Speaking on Friday, Gardner also accused the incoming Trump administration of "breaching" diplomatic procedure in the transition of diplomatic staff.
Gardner, who has been in post for three years, will step down on 20 January.
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He reserved his biggest criticism for Farage, who, he revealed, had written to him asking to meet.
In a remarkably outspoken attack on the man who spearheaded the Brexit campaign in the UK, Gardner said he regards it as "unfortunate that Farage appears to hold some influence" with the incoming US administration.
When asked by this website, what advice he might give Farage should the Ukip MEP be appointed UK ambassador to Washington, Gardner said, "That is not worth talking about because it is not going to happen."
But he said he would "not be shy" in speaking up for the "50 years of support" the US had provided for EU integration, adding, "Nigel Farage is one voice but I don't believe his is a representative or typical voice.
"His is a fringe voice which I hope people will not listen to. His views are a polar opposite of mine. I take great exception to some of the things he has said which are quite unacceptable."
In a particularly scathing assessment of Farage, he added, "The message that he disseminates is a caricature."
Gardner went on to appear to ridicule Farage's request to meet him before he leaves office later this month.
On the letter Farage had written to him, Gardner said, "He seemed to use the word 'your excellency' a lot. In fact, he used it half a dozen times."
He said that while he had met many MEPs and other senior EU officials during his stint in Brussels, he had never met Farage and declined to be drawn on whether he would take him up on his offer.
Reacting, Nigel Farage said, UKIP MEP Nigel Farage said, "Gardner's comments are the last desperate defence of Obama's pro-EU policy.
"It is very important that Trump gets rid of this type of thinking and gets with the modern work. It is clear that Trump's new team is realistic and already asking which member states will leave the EU next."
Gardner, in a wide ranging briefing, also made a robust defence of the EU and appealed to senior EU leaders, including Angela Merkel, to do the same.
He said, "One of the first questions I am often asked, after the EU referendum in the UK, is which country I think will be next to leave the EU.
"The perception appears to be that 2017 will be the year when the EU falls apart. Despite all the issues and challenges it faces, I do not believe the EU is going to fall apart."
Gardner, who promised to speak his mind in supporting the European project, criticised those, including in the incoming US administration, who looked on the EU as a "dysfunctional group of countries."
"This is a fundamentally flawed approach," he declared.
He also believed that "faith" in the EU is returning, saying, "If you look at the most recent polls, they show that support for the EU is on the increase. I think this is because people, after the Brexit vote, realise what is at stake."
Those pressing for fragmentation of the EU, he said, are guilty of "sheer folly."
The EU, he told reporters, had "stepped up to the plate" in several areas, including militarily in recent times, adding, "A strong and convincing case can be made for the EU but we need to use what I call less fuzzy language in doing so."
On Brexit, he said, "I do not want the US to be the cheerleader for Brexit, particularly one that increasingly looks like being a disorderly and disorganised Brexit.
"A hard Brexit, as looks likely, will be bad news for US business and this is something I will be not shy on speaking about."
He also said diplomatic procedure had been breached by the incoming administration, by the failure to give staff at the embassy in Brussels and other cities the normal termination notice.
"I received a cable on 23 December saying we had to be gone by 20 January. It is very short notice and an inappropriate period of notice."
Gardner will take up a three month stint at the College of Europe in Bruges before returning to London, where his children live.