Ireland had never before beaten New Zealand away from home before that series in June 2022, where they bounced back from losing the first Test to win the next two.
And ahead of a potential quarter-final clash between the two sides at the Rugby World Cup, Barrett said the All Blacks are desperate to make amends.
"We learnt a lot during that series, it was a challenging time, some of the most challenging times we've faced as an All Black team, and personally, losing the series in our back yard," said Barrett.
"What we know is the beast that Ireland are and if you allow them to dictate up front and play the way they want to, they're a tough team to stop.
"So, if it's Ireland in the quarter-finals, it's going to be great because there are a lot of us who are pretty keen to get one up on them and still we're hurting from what happened last year."
New Zealand booked their quarter-final place with a 73-0 thrashing of Uruguay in Pool A on Thursday.
They will play either Ireland, Scotland or South Africa in the quarter-finals, depending on other results this weekend.
Although New Zealand ran in 11 tries on Thursday night, it took them 20 minutes to snatch the first.
Uruguay were highly competitive in that opening quarter and forced several turnovers and handling errors from the three-time world champions.
'We got an uppercut'
Head coach Ian Foster admitted he was worried about how his team handled that pressure, given they will face a lot more in the quarter-finals.
"Is that a concern, yes it is," said Foster.
"Us coaches, we worry about everything, so we didn't like that start.
"We expected that start, we knew they would try to turn the contact area into a bit of a free-for-all and really try to get under our skin in that space.
"I think it was a mental looseness that we started to look for some passes and stuff that weren't on."
Foster said it was a "mindset issue" but insisted he was pleased his team managed to turn it around after 20 minutes and slip seamlessly into their stride.
The head coach said New Zealand have learnt important lessons from their series defeat to Ireland, and one of those was that they needed to improve their defence against the line-out maul.
"I don't think we got surprised in that series but we realised there were a couple of areas that our benchmark wasn't high enough," said Foster.
"You cant give top teams a couple of line-out drive tries against you per game and expect to come out and beat them consistently.
"So, we had to work hard on a couple of areas -- that obviously being one -- and I think we did and I think we know we're (still) going to get massively tested in those areas.
"It was an uppercut we got and, to be fair, we've had those uppercuts before and sometimes you get an uppercut but you just have to come out on the winning side of it."
