Brown's first match as captain ended in a 51-22 defeat by New Zealand on Sunday with a slack period in the first half proving their downfall as the All Blacks notched up three converted tries in 10 minutes.
South Africa began their November series with a 16-12 win over Ireland and Brown is confident Scotland can give the Springboks a close game.
He said: "There is no doubt there is improvement to be made. We have looked at the video and we know the areas that we need to work on. We have been doing that in training and I'm very confident we can put it right on Saturday."
Much was made of the 25 missed tackles during Scotland's defence against New Zealand but Brown feels the problem was one deeper than individual errors.
The former Glasgow forward said: "It's something we have looked at and worked on this week, but I think it's also the case that our shape and our structure wasn't quite spot-on so that was really isolating guys in the defensive line and putting them under pressure. We have looked at it and worked on it and I'm sure we will be much improved on Saturday."
Scotland have recent experience of making exactly the sort of improvements they need. Andy Robinson's men hosted South Africa two years ago on the back of a 49-3 thrashing by the All Blacks and stunned the then world champions with a 21-17 victory.
All of Scotland's points came from the boot of Dan Parks, who has now retired from international rugby, but Scotland have a fresh attacking weapon in the form of Dutch-born Edinburgh wing Tim Visser, who took his international tally to four tries in three Tests with a double against Steve Hansen's side.
And Brown believes a repeat is not out of the question - if Scotland can plug the gaps.
"There's no doubt it's possible," the 30-year-old said. "We know what happened two years ago but in saying that so do South Africa. So they will be looking for a bit of payback and it's up to us to make sure we really nail the level of performance that we need to to be successful.
"It was a great win, on that day I think it was based on a really solid defensive effort. We will need to make sure that we are really tight in that aspect of the game and make that work for anything that they get, and when we're on the attack we need to ask them questions and put them under pressure."
Brown, who has been moved from number eight to openside flanker after Ross Rennie suffered a shoulder injury against New Zealand, has more experience of South Africans than that one match two years ago.
Eight of his Saracens team-mates are South African-born, including England international Mouritz Botha, with hooker Schalk Brits among the tourists' replacements on Saturday.
"They are a really, really good bunch of guys," Brown said.
"Obviously there is a bit of banter flying around but they are really, really happy that I'm in the Scotland side and we're all just looking forward to Saturday. "I have managed to pick up a small amount of Afrikaans.
"Sadly most of it is swear words, which actually might be okay on Saturday."
And Brown has not ruled out throwing in some of his language skills to catch his opponents off guard at Murrayfield.
He said: "I did last time actually. I said one phrase which wasn't even a swearing phrase and I think he was slightly shocked when I came out with it."
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