But Barnes also called on Kiwi rugby fans to give South Africa more credit and understanding in desperate circumstances.
The Cheetahs are playing under the threat of extinction with two South African teams to disappear in the revamped competition.
Rennie said the Cheetahs "showed in the first 25 minutes why teams like that should be in the comp.
"There is a lot of nervousness here, people uncertain about their future. The Cheetahs were desperate with all the talk in the media, and we thought we were ready for that sort of onslaught."
Barnes said: "We were probably lucky to only be 24 - 0 down - the other team is fighting for survival, you can see that from the way a lot of South African teams are playing. I take my hat off to them and their coaches.
"They (the Cheetahs) scored a couple of cracker tries. You saw the Stormers last week...they would have knocked over any team that day. Back in New Zealand, we need to give some of these teams more credit.
"Their coaches are doing a bloody good job over here, to get teams to this level. A fair bucket load of their players have trucked off overseas, there is a continual turnover of players, but they've shifted a long way in the last 12 months."
Barnes said senior players read the riot act at halftime, about "what we are about, what it means to be a Chief".
"There are a couple of games in a row now where we haven't been happy with the start. But the boys showed a lot of character.
"You are on the high veldt, down 24 - 0. A lot of teams would have dropped their lip but we stayed calm, got back on with the job."
Meanwhile, All Black centre Anton Lienert-Brown (leg) is in doubt for Saturday night's match against the Western Force in Perth and flanker Mitch Brown will be monitored over concussion.