Ireland was comprehensively defeated in the first Test against the All Blacks, losing 42-19, but responded with a 23-12 victory in the second meeting to claim their first away win in New Zealand on Saturday.
Victory in Dunedin teed up a winner-takes-all decider at the Sky Stadium in Wellington next weekend, with New Zealand looking to set the record straight and seal the series win on the North Island.
While Farrell expects another tough task, the 47-year-old insists Ireland will not shy away from the challenge as they fancy themselves against any side in the world.
"We always get a response, don't we?" he said. "Everyone knows that, history tells you that. We're used to it by now. We'll look forward to that.
"We've created a little bit of history for ourselves, little old Ireland, but we've earned the right to take it to the last weekend to see what we can do in the final week.
"The players back themselves against anyone and the more we can keep giving them, these occasions of playing the best teams in the world, the better they're going to get."
The task for Ireland in the second Test was somewhat eased by the first-half dismissal of New Zealand prop Angus Ta'avao.
Ireland did have to absorb some pressure in the second half, though, and Farrell pinpointed its defensive resolve as proof of the continued development of his side.
"I suppose the most impressive thing that we are doing pretty well at this moment in time is understanding where we're at, each moment at a time and staying calm and not getting too overawed or frustrated with errors or decisions or not executing," he continued.
"We're pretty good at trying to stay neutral and stay on task and it's helping us to play in these big games and compete."
A second-string Ireland team were defeated 32-17 by the Maori All Blacks at the end of June in Hamilton, and Farrell also plans to offer those players a chance to make amends against the same team on Tuesday.
"There are bigger things to think about in regard of this tour for us," he added.
"We've some young lads in that changing room that have been inspired by these lot [the Test team], who want to get back out there again on Tuesday night and perform well against the Maoris.
"These lads have taken a lot of pain, that's what we've put them under, the pressure of taking them out of their comfort zone.
"The weeks have been totally different to what they've been used to before because of us trying to play five games in such a short space of time and there's been no whinging.
"They've been mentally really tough and they'll back the lads up as well to make sure they're in good form for Tuesday night."