Employees across the country will get a one-day paid holiday for Islamic New Year
The five-time winners appeared to be heading for defeat when they were reduced to 79-5 at Trent Bridge on Thursday following a hostile spell of fast bowling by the West Indies
But, with Nathan Coulter-Nile hitting a career-best 92 and Steve Smith making 73, Australia recovered to a competitive 288 all out.
Despite fifties from opener Shai Hope and West Indies captain Jason Holder, West Indies fell 15 runs short in their reply, with Starc taking five for 46.
"We haven't played awesome cricket in that game, we played well in patches but we can get better," said Starc.
"It's exciting to find new ways to win. Coults (Coulter-Nile) played very well to get us to a competitive total."
He added: "You always have to be confident in those situations, it was touch and go for a while. We always had the belief. There is lots of good bowling in our line-up and we were only a couple of wickets away."
Left-armer Starc, 29, removed the dangerous Chris Gayle before he could really get going and also took the crucial wickets of Andre Russell and Holder.
Starc was the player of the tournament when Australia won the 2015 World Cup on home soil, taking 22 wickets.
"The experience of four years ago plays a part, but for guys who can bowl at the death we have a lot of options," added Starc.
Former Australia captain Allan Border said an in-form Starc was the "best around".
"The way he starts, he swings the ball early, and then later on he goes around the wicket and makes it hard for tail-enders to get bat on ball with his pace and the angle he bowls," said Border, who led Australia to the first of their five World Cup wins in 1987.
West Indies batsman Shai Hope, who made a painstaking 68, admitted the manner of West Indies' loss at Trent Bridge was tough to take.
"This is going to be a tough pill to swallow having basically been dominating the game for the majority of it and then not being able to cross the line," he said.
But said the West Indies should keep faith with a policy of aggressive short-pitched bowling from the pace quartet of Oshane Thomas, Sheldon Cottrell, Carlos Brathwaite and Russell.
"Most definitely, as long as you get wickets with the new ball you always put teams under pressure," Hope said.
"It was just unfortunate we couldn't drive home and get the tail in a bit earlier."
Employees across the country will get a one-day paid holiday for Islamic New Year
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