Indian seamer Bumrah took 5-27 after South Africa had won the toss and elected to bat, with several players getting into the 20s and 30s before losing their wicket.
India reached 37 for one at the close of play and trail by 122 runs, with Yashasvi Jaiswal dismissed for 12, and Prince admitted most of his side's wickets fell to good balls on a surface that was up and down from the first over.
“Probably after four or five deliveries in the first over, where one rolled and went for four byes, and two or three reared up, the signs were there pretty early on that the bounce is not consistent,” Prince told reporters.
“But it was a sensational bowling display, particularly from Bumrah. He was relentless, and the spinners were pretty good as well. There were a lot of good deliveries and sometimes as batters, there is not a lot you can do about them.
“We have to work hard and bat better in the second innings. There is a long way to go in the game.”
Prince said that inconsistent bounce plays havoc with a batter’s mindset and this may have played a role in their collapse on day one.
“We encourage batters to play their options and back themselves in whatever their attacking and rotation options are. They must be true to themselves and play their game,” Prince said.
“But if you don’t trust the surface in terms of consistency, it can create doubts such as, ‘Should I hit the ball over the top? Will it hit the bottom end of my bat?’
“When you expect batters to get to 20 or 30 and then grow in confidence, none of the batters could do that because of the inconsistency of the bounce. You don’t trust the surface as much as you should after spending an hour at the crease.”
Prince did say he would have discussions with each batter on how to manage their time at the wicket in the second innings.
“We will have some discussions about which types of options we can take. Every batter comes with his own mentality and strengths when he comes to the crease. Everyone has their own character and we trust people to play within their character.
“But obviously we have to take the surface into consideration next time round. These are the conditions and how can we play effectively within that.”
There was a moment in the day’s play when Bumrah and wicketkeeper Rishabh Pant gathered to discuss a leg-before-wicket review against South Africa's 5 foot, 4 inch captain Temba Bavuma, with the bowler overheard on the stump microphone saying, "Bauna bhi toh hai ye", meaning "He is a dwarf too."
Prince was asked about the comment, viewed in some quarters as derogatory, but said he was unaware of it until it was brought to his attention in the press conference.
“I don’t think there will be any issues with what has been said out there.”
South Africa started the match without key fast bowler Kagiso Rabada, who injured a rib in training and failed a fitness test on the morning of the match.
He will be assessed ahead of the second Test that starts on November 22.