South Africa won the third test in Barbados by an innings and 86 runs on the fourth day, earning an unassailable 2-0 lead in the four-match series.
"Before the series everyone wanted to know how we were going to take 20 wickets in a match," Smith told a news conference.
"We've gone out there and made the pitches do things, we've hit these decks hard.
"You've really got to work hard on these pitches."
South Africa declared their first innings on 548 for nine early in the morning session leaving West Indies to score 252 to make the visitors bat again but the home side were dismissed for 166 in the 10th over after tea.
Fast bowler Andre Nel was the pick of the South African bowlers taking a career-best six for 32 in the second innings to complete match figures of 10 for 88, his first 10-wicket test haul.
"We spent the first three days setting up the match, and this morning the bowlers came out and did the job," Smith added.
"It was outstanding to see the guys run in and bowl like that on a flat wicket."
The win over West Indies was South Africa's first away triumph since they beat Bangladesh in 2002-03.
"I think we've taken some big steps last year and over the last eight or nine months," Smith said.
"We'll certainly celebrate this win, because we've learnt that you can't take a test win or your own form for granted."
SUPERB FIGURES
Despite his superb figures, Nel refused to take the all of the credit
"All of us bowled well, and I was lucky to pick up the wickets," Nel said.
The aggressive bowler took the key wickets of Brian Lara and Shivnarine Chanderpaul in consecutive overs after lunch.
"My tail was up after I got Lara and Chanderpaul out, Graeme struggled to get the ball out of my hand after that," he said.
Nel has now dismissed Lara eight times in the 12 test innings.
"I like a challenge, and I try to raise my game to get the top players out," Nel added.
"That's the only way you can improve. I run in and try my best, and I play with my heart."
West Indies captain Chanderpaul was at a loss to explain his team's performance.
"Our bowling hasn't been good, and most of our batsmen haven't been focused," he said.
West Indies coach Bennett King said his team needed all-round improvement.
"It's very hard to win or even be competitive when your top three are making scores like 12 and 17," King said.
"We need to bowl like we did yesterday (on Saturday) and we would love to have a spinner who can take key wickets.
"That's a wish list."
The fourth and final test starts in St. John's, Antigua on Friday.
