Cummins added he was proud of the team for “clawing our way back, kind of grinding it out, and then once we had the lead, you know, not giving it back”.
“I think our standards were very high for the last three or four days,” he added.
South Africa skipper Temba Bavuma said his players needed to learn from the way Australia played after his first loss in 13 tests as captain.
“They showed their experience, they showed their skill to get themselves into a very competitive position.
“You don’t want to give them that opportunity to play the game from the front.
“We had the opportunity to prepare as well as we could.”
“I think a lot of the mistakes we made out there were mental,” he added after South Africa’s first test in 11 months.
Record-breaker Smith
Opening batsman Aiden Markram defied the bowlers for a minute short of six hours, scoring 75 before he was ninth out, caught behind from an inside edge off Mitchell Starc.
The last four wickets fell for five runs in the space of 16 deliveries against the second new ball.
Markram and Wiaan Mulder (29) were largely untroubled as they batted through the first 110 minutes of the day.
But a double bowling change brought two wickets.
Mulder was caught down the legside by wicketkeeper Alex Carey off Hazlewood for 29 after a 139-minute innings during which he faced 110 balls.
Renshaw came on to bowl his off-spinners in the next over and with his first ball dismissed Kyle Verreynne for a single when the South Africa wicketkeeper played a forcing shot against a wide ball and edged a catch to Steve Smith at slip.
It was the continuation of a dream match for Renshaw, who top-scored in both innings with 190 and 82, then took his first test wicket when he dismissed Bavuma on Monday.
It was Smith’s fifth catch of a match in which he became the world record-holder for most catches by a fielder in tests.
Smith was back in action after being off the field at the start of South Africa’s innings on Monday following a blow on the head while batting.
Marco Jansen made 35 and added 45 with Markram before Hazlewood bowled him in the fourth over with the second new ball.
Three balls later Simon Harmer gloved a sharply lifting ball to Carey.
Australia were in trouble with the bat on the first day but dominated the rest of the match after Renshaw steered them to a first-innings total of 390.
South Africa will need to bounce back quickly in the second test of the three-match series in Gqeberha starting on Sunday, when Bavuma hinted that key fast bowler Kagiso Rabada would likely be fit to play.