Best told The Irish Times, "That first victory against New Zealand, in Chicago, it felt like we pushed through a ceiling.
"But it was hugely important to get the second one, to prove again that we can do it.
"We want to be a team that can prove we can beat anyone and we've not just shown it once, we've shown it twice," he said.
At the same time Ireland must also make the most of the reality check they received when only able to claim third place in the Six Nations this year if they are to succeed at the World Cup.
Instead, the players must look to the Grand Slam they achieved in their 2018 campaign and apply that to Japan.
Ireland play their first World Cup warm-up game against Italy at the weekend and Best said the side were as hungry as he had seen them during coach Joe Schmidt's time at coach.
"It sometimes takes a reality check, and finishing third was bitterly disappointing. So coming in at the start of this pre-season everyone is as hungry as I have ever seen them.
"We've had a group of players that want to prove that the 2019 Six Nations was the blip, not 2018," he said.
As well as playing Italy, Ireland will play Wales twice and England once before opening their World Cup programme against Scotland.
While he will be 37 when the Cup begins, Best said after a gruelling pre-season he was feeling good for a tournament which he felt was wide open.
"New Zealand are the best team in the world and they are the favourites. But I also think this will be one of the most open World Cups.
"Anyone will feel they can beat anyone on their day. And it's great that Ireland can be one of those teams.
"But we also know that, look at Wales and England in the Six Nations, we can lose to those teams too," he said.