A brilliant victory over Tri-Nations champions and tournament second favourites Australia indicated the Irish can be major players in New Zealand.
Following on the heels of denying England the Grand Slam in March, it was evidence the team has the ability to significantly lift their game against top opposition.
However, Best insists the challenge now is to improve for the remainder of Pool C as well as the knockout stages.
"The good thing about this team is that when big games come there are big performances in us," the Ulster hooker said.
"There's no doubt when you look at the calibre of players we have, and you look at what we've achieved in the past, that we have big performances in us.
"The big pressure for us now is to show it consistently. It can't be one big game followed by a couple of mediocre ones.
"From here on it must be big performance after big performance. It's a short tournament and we must raise our game every time.
"It was great to get a win against Australia but now we must make sure it's worth something come the end of the group.
"Our belief was never in doubt, but it's undeniable that beating Australia has given us a great chance to top this pool.
"It's put it all in our hands and it's up to us to take this chance. We need to be ruthless to enable us to kick on from here."
Four successive defeats in the warm-up games ensured that little hope existed outside the Ireland camp that Australia could be toppled.
But Best insists last month's results had minimal impact on the belief of the team that they could perform at the World Cup.
"We go out to win every game so there's no doubt we were disappointed to lose those matches," he said.
"But we knew there was a bigger picture. There were aspects of our game we were happy with and there were aspects we needed to work on."
One of the highlights from Eden Park was the potency of Ireland's scrum, which has now become a key weapon in their arsenal.
The Wallabies conceded five penalties from the set piece, two of which were punished by the boot of Ronan O'Gara.
Best added: "The scrum is a head on head on collision and if you get the upper hand in that arm wrestle... Teams have got on top of us in the past and it is quite tiring mentally. When you concede a penalty at a scrum you feel drained.
"There's no doubt that scrummaging performance took it out of Australia's back five around the pitch.
"Because they're such potent and destructive carriers we knew we needed to zap them a bit there.
"In the past we've been guilty of letting teams off the hook a bit in the scrum, but we were unrelenting and that's something we must keep up.
"We've strived to make the scrum a weapon. It's a good feeling to know that if we get it right, we can have a good day.
"We're starting to gain confidence in the scrum with every game that goes by."
Paul O'Connell and Gordon D'Arcy sustained hamstring strains against the Wallabies, but have yet to be ruled out of Sunday's clash with Russia in Rotorua.
"The progress of both players will be monitored over the coming days," an Irish Rugby Football Union statement read.
"No decision on their availability for the game against Russia will be made until the team is announced on Friday."
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