The All Blacks saw off the cream of British and Irish rugby with 3-0 series triumph during the summer and Byrne believes victory on Saturday would go some way towards avenging those defeats.
And the veteran front row, who started the first and third Lions Tests, insists Tri-Nations champions New Zealand are far from invincible - despite their emphatic 41-3 win over Wales last Saturday.
"I can't wait to play these guys again. In the summer we came off the pitch feeling it was our mistakes which cost us. If we hadn't made those mistakes maybe the games would have been tighter," he said.
"It's a similar situation to Ireland's tour to South Africa last year - we lost both Tests which meant everyone was chomping at the bit when they came to Dublin in November, a game we won.
"We've got things to put right against New Zealand. They're not unbeatable, as South Africa proved during the Tri-Nations in the summer.
"Nobody gives us a chance against New Zealand. We have to prove people wrong. I couldn't care less if they have made 15 changes. If we win, it will go down in the record book that we beat New Zealand."
Byrne's memories of the Lions' series are more painful than most after the tourists' line-out troubles in the opening Test, with Ireland's hooker shouldering much of the blame.
"It's amazing how much something like that can hurt you because that first Test was seen as a complete disaster for myself," he said.
"I took the criticism on the chin. My responsibility was the line-out and every facet of that broke down. The quality was there in our line-out so I felt we should have got nearly every one on our own throw.
"Luckily that wasn't the end of it as I was involved in the final two Tests. I'd say the Lions pack in the third Test got on top of the All Black pack, but that wasn't reflected in the score."