Shami took nine wickets in the match, the second best figures for an Indian bowler on debut, as India bundled out the visitors for a paltry 168 in their second innings to win the match by an innings and 51 runs.
"It was the disciplined bowling that really helped us. Shami was fantastic, the line he bowled I think the most of the fast bowlers had got the reverse swing but he got the right line and length and that was the key. I think that's the reason he got nine wickets in this game," Dhoni said at the post-match presentation ceremony.
"You need a bit of pace if you want to dominate, he has very good seam positioning which means he can reverse away from the right-handers too. On a wicket that has more bounce he can move the ball both ways," he added.
Dhoni also praised all-round performance of off-spinner Ravichandran Ashwin, who became the first India player to hit a hundred and take five wickets in Tests twice.
"He bowled a disciplined line and length, he did not try too many things. It really contributes overall as a bowling unit. It helps the other bowlers because they are not giving away too many runs. Overall, I am happy with the performance.
"If you look at the way cricket is played these days, if your 8, 9, 10, 11 players can contribute, then it becomes a key factor if you have a partnership lower down the order. Ashwin batted beautifully...like a proper batsman. He has really proved it at the Test level and it's good to see the way he batted with Rohit and got the partnership going," Dhoni said.
Rohit Sharma, too, made his debut special by cracking a magnificent 177 and Dhoni wants the young batsman to take more responsibility.
"You have to believe in destiny. In Nagpur, there was a game in which he was supposed to play but during a warm-up session he injured his ankle just before the match. We all know he is very talented and now it's reflected on the field too. He is really enjoying his cricket which is the key. Hopefully, as we go ahead, he takes more responsibility."
Dhoni said the second day was the worst to bat but the wicket eased out as the match progressed.
A dejected West Indies skipper Darren Sammy lashed out at his batsmen for the meek surrender.
"We get ourselves in good positions in Tests and then we give it away. Even when India were batting, we were in a good position at lunch yesterday and then we gave it away. Getting bowled out in 60-70 overs is not good. One of our goals was to bat at least a 120 overs and we didn't do that," he said.
Sammy though was happy with Shane Shillingford's impressive show. The off-spinner claimed six wickets in India's first innings.
"I think the credit must go to Shillingford, he bowled long spells, to bowl 50 overs is a lot. The other bowlers should have backed him up more, myself included. The combination is one we have used in the Caribbean but we'll see what the best XI for Mumbai is," he added.
Man-of-the-match Sharma said it was difficult to bat under pressure as the runs were not coming off easily.
"It wasn't easy to bat, runs weren't coming easy for us. We just wanted to stick out there and capitalise on loose balls which we did. We knew we had to extend the partnership as much as we can to get a lead," he said.
Rohit waited for six years and 108 ODIs to make his Test debut and the 26-year-old said it was worth a wait for him.
"All I can say, it (the wait to make debut) was worth it, it can't get better than this, such a memorable match, really happy with what we have achieved."