The Irish claimed a landmark 2-1 tour triumph following a spellbinding first-half display in Wellington on Saturday, which paved the way for a 32-22 victory in an epic third-Test decider.
Tries from Leinster trio Josh van der Flier, Hugo Keenan and Robbie Henshaw helped the tourists lead by 19 points at the interval before Rob Herring extinguished a Kiwi fightback sparked by scores from Ardie Savea, Akira Ioane and Will Jordan.
England's former dual-code international Farrell - a two-time Man of Steel during his rugby league days - was left beaming with delight by a result which moved Ireland top of the world rankings.
"It's difficult for me because it is not mine, it's theirs," said Farrell, saluting his players. "They've grabbed hold of it hugely.
"Some of the stuff they've done out there today, we've done it together so I suppose when you look at it like that it's the most proud that I've ever been part of a group, without a shadow of a doubt.
"Pleased? I don't think that's the word. I mean, what's the biggest thing that you can say about a group of people? I don't know if there is a word.
"This is the hardest thing you can do in rugby by a country mile, especially when you take it down to the last game and we know from history that the All Blacks are going to come out firing."
Farrell became the first visiting coach to orchestrate tour success over New Zealand since France prevailed 2-0 in 1994.
Ireland had never won away to the three-time world champions before last weekend's milestone 23-12 victory in Dunedin cancelled out a 42-19 drubbing in the Auckland opener to set up a tantalising climax.
Captain Johnny Sexton once again led by example and, in the week he turned 37, celebrated another personal milestone.
The influential fly-half contributed 12 crucial points to become only the second man - after Ronan O'Gara - to reach 1,000 in the green jersey.
"It doesn't get much better than this," he said. "By saying that, it's the biggest respect we can give New Zealand.
"The celebrations probably weren't the most humble but that shows how much it means.
"It is just very, very special and it's a special group led by Faz (Farrell). It's great to be a part of.
"I'm sure there's lots of smiling faces across the country. We speak about it all the time, primarily family at home but also the people of Ireland that we represent. I don't think they could be much prouder."
But defeat for New Zealand was their fifth from the past eight meetings between the countries to heap further pressure on under-fire coach Ian Foster.
Foster, who has now lost seven of his 24 games in charge, refused to discuss his future.
"I just want to talk about the Test match," said the 57-year-old.
"I want to congratulate Ireland on a series win here. They're a quality rugby team and they're a big test for us and, at the end of the day, we fell a bit short. Clearly we've got a little bit of work to do."
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