"I said to the players, 'You're in some rare company in terms of Australian rugby'," McKenzie told the Sunday Telegraph.
"That doesn't sound like much to people but we bump into the All Blacks regularly and it's been hard to get momentum in the last 11 years.
"Not only have we got the chance to compete with the Bledisloe on the line, but we also get a chance to extend that number of seven.
"They're the type of things that are hard to achieve, but you get that by doing some spectacular things on the field against the next opposition - two in a row against the All Blacks and then the Springboks.
"To get to 10 would be a fair achievement.
"All we can do is set ourselves up for that, and I think we can set ourselves up pretty well. We've got our own little winning streak going, we'd like to keep that going.
"If the All Blacks want to get distracted by [their record attempt], or if that becomes a millstone around their neck, well fine. But we won't be talking about that."
The All Blacks and South Africa jointly hold the world record for tier one nations with 17 wins in a row each.
New Zealand achieved the feat in 1965-69, and South Africa matched it with their all-conquering side of 1997-98.
The All Blacks have come close three times in the past eight years before falling short.
They put together 15 wins in a row in 2006, 15 in succession in 2010and in 2012 put together 16 wins in succession before they were foiled by the Wallabies, who scraped out an 18-18 draw in Brisbane.
The All Blacks, who went undefeated through 2013, want to be the first team in history to go unbeaten for two years and, after seeing off England 3-0 in June, will arrive in Sydney for the August 16 Bledisloe showdown with history in their sights.
But with the Waratahs and Brumbies having made the Super Rugby semifinals - the first time two Australian sides have featured in the final four since 2002 - there's a growing air of confidence in Australia.
"We'll get confidence out of what the Super Rugby teams, and confidence out of what the Wallabies have been doing," McKenzie said.
"That's about all we can muster, apart from tactics on the day and getting our selections right.
"We've set ourselves up to do better than we have in the past.
"Now it's about getting out there and doing it."