Lanning gave a sharp chance to square leg on 62 but that was her only dodgy moment in a high quality knock. Alex Blackwell added some lusty hitting to be 50 not out as Australia cruised home to win by six wickets.
The White Ferns bowlers toiled away well enough, with pace bowler Lea Tahuhu impressing in all three games but Lanning was just too good in the end.
"I guess we are disappointed to lose today. It is a hard pill to swallow but Meg Lanning and Alex Blackwell played well. The way we have played the three games I have been really proud of how we have stood up when it has been tough. We have shown we can compete," Bates said.
On a personal note she was pleased with the consistency she showed with the bat in scoring 41, 63 and 110 against the world's number one rated side.
"I am pleased with how I batted over the three games but I would have taken a win over any hundred. It was pretty tough out there but it would have been nice to get 260-odd which, perhaps, if I had batted a bit deeper and been not out at the end, we could have done."
The White Ferns picked up two ICC International Women's Championship points for winning the first ODI on Saturday to join the West Indies behind Australia, with the top four nations qualifying automatically for the 2017 World Cup.
"Those two points were huge for us. We picked up four against England and that was pleasing. We've got South Africa and Pakistan coming up so we will be looking forward to moving up that ladder and qualify for 2017," Bates said.