A rampant Kagiso Rabada took six for 50 as the West Indies, set to make 247 to win, were bowled out for 159 at SuperSport Park in Centurion.
South Africa earlier lost six wickets for 67 runs when they were bowled out for 112 in their second innings – a new low against the West Indies.
"The bowlers ticked a lot of boxes and showed a high level of skill," said Bavuma.
"But there is definitely room to improve in the batting. We have been having those conversations for quite a while.
"The batters will be having a conversation about our game plans, how we adapt to conditions and how to do better next time," said Bavuma, who himself faced only three balls in making a 'pair' on his Test captaincy debut.
Conditions were difficult for batsmen against two strong fast bowling attacks, with inconsistent bounce and sideways movement, but both captains said they did not excuse the low scores.
"Our batting unit only batting for just over 100 overs in both innings is where we missed out," said West Indies skipper Kraig Brathwaite.
When it was suggested that the difference between the teams was South Africa's strong start in the first innings – they reached 221 for one before being bowled out for 342 – Brathwaite defended his bowlers.
"I thought the bowlers did a good job," he said.
"The first two sessions, South Africa batted extremely well. The bowlers really pulled it back in the third session. Then to bowl out South Africa for under 120 runs (in the second innings) was a top effort."
Brathwaite said more net practice was not going to make a big difference.
"Mentally, we've got to be clear on which balls you play and which balls you leave."
Jermaine Blackwood stood virtually alone against Rabada and the other South African fast bowlers on Thursday, making 79 before he was ninth out, fending Rabada to second slip.
South Africa opener Aiden Markram was the Test's top scorer with 115 in the first innings and 47 in the second, and was named player of the match.
Having been dropped last year after a run of low scores, Markram welcomed his return to the top of the batting order.
"It's where I've been for most of my Test career," he said. "Credit must go to the coach (Shukri Conrad) and captain for backing me in that position. It gave me a lot of confidence."
Bavuma described South Africa's collapse from 31 for no wicket to 49 for four on the second evening as "crazy hour" but said he always had confidence in the ability of the bowlers to defend whatever target the West Indies were set.
"The ball was nipping about and there was variable bounce. With our attack we were well equipped to exploit those things," he said.
Bavuma said the extra two days off before the second Test, starting at the Wanderers in Johannesburg on Wednesday, would benefit the bowlers.
"The biggest thing for the bowlers is to rest, to get off their feet. It was a big effort by them."