A spin-heavy attack of Ravindra Jadeja, Kuldeep Yadav and Ravichandran Ashwin collectively took six wickets and gave away 104 runs in 30 overs to dismiss five-times champions Australia for 199, before India sealed victory after a nervy start.
Finch, part of the Australian team who won the 50-overs trophy in 2015 and led them to Twenty20 World Cup success in 2021, said they should not have allowed the trio to bowl how they wanted to on a helpful Chennai wicket.
"Part of it comes down to how India bowled spin, but we also need to look at the way Australia batted," Finch wrote in a column for the ICC website.
"There was a clear plan among the group to be proactive, to try to limit dot balls and rotate strike against what they knew would be a world-class group of spinners.
"There was a bit of a lack of aggression from the Australian batters. They will be disappointed by the intent they showed and the fact that they weren't able put any pressure back on India.
"It needs a mindset shift, to look to be on the front foot a little more and take some calculated risks."
Finch said the defeat was not "fatal" as Australia prepare to face South Africa on Thursday.
"The mood around Australia is still optimistic. With a nine-game group stage, you can afford a little slip-up here and there and it's not fatal," Finch said.
"In the Twenty20 World Cup, we found that losing one game is enough and the margins are so fine.
"Here you can cope with a couple of losses, you just don't want them to be too big for net run rate."
