Smith's men are top of the tri-series table on nine points after their 36-run victory over South Africa on Saturday.
David Warner (109) guided Australia to 288-6 in Basseterre before a dramatic fight back when defending the total.
South Africa were 210-3 in their chase before an incredible collapse saw them bowled out for 252 in the 48th over.
Mitchell Starc (3-43), Josh Hazlewood (3-52) and Adam Zampa (3-52) were the main destroyers.
Smith was full of praise for his bowling group as a whole, with leg-spinner Zampa drawing particular plaudits
"It's always hard to start against a ball that's reversing when you've got someone like Mitchell Starc or Josh Hazlewood coming in at you," Smith said, via ESPNCricinfo.
"I thought those guys did a terrific job when the ball started to go. I think we got five wickets in six overs at one point and that obviously turned the game.
"[Zampa] was good. I put him under a bit of pressure at the end there as well. I bowled him a few overs where they could have hit a few to these small straight boundaries.
"But he held his nerve nicely. He changed his pace, mixed it up, bowled some googlies and he's come a long way."
Australia's next outing is a clash against West Indies on Monday, with the hosts bottom of the table.
The biggest concern for Smith is a finger injury to Warner, who hurt himself in the field against South Africa.
The explosive left-handed opener expects to be fit, but more is expected to be known on Sunday.
The Windies were last in action on June 5, when they suffered a comprehensive six-wicket loss to Australia.
Sunil Narine has been the standout bowler in the tri-series, taking eight wickets at an average of 7.87.