Scotland have no chance of equalling their third-place finish from last year ahead of their final game in Wales on Saturday, although they could match their four-point tally.
However, Scott Johnson's men would need to win by 20 points in Cardiff to avoid their seventh bottom-two finish in eight years.
Johnson has been aiming to make Scotland more competitive before handing over to Vern Cotter at the end of the season, when the current Clermont Auvergne coach steps up and attempts to prepare the squad for the 2015 World Cup.
Scotland suffered heavy defeats to Ireland and England in their opening two games, scoring just six points in the process, but have turned their form around to be far more competitive against Italy and France.
However, a late and narrow win in Rome was followed by a very similar defeat against France at Murrayfield.
Brown said: "If you look at the stats and the performances over the course of the Six Nations, I feel we have definitely improved.
"But we know that we need to keep on with that improving, because whilst we are improving, so are all the other nations. We need to keep on working hard and pushing the bar higher and higher.
"We certainly take a lot of confidence from the last two performances but we didn't win on Saturday."
Scotland were heading for victory following first-half tries from Stuart Hogg and Tommy Seymour but a misplaced pass from Duncan Weir let in Yoann Huget to score against the run of play, and the French stole a 19-17 win thanks to Jean-Marc Doussain's late penalty after Tim Swinson was controversially penalised for failing to release at the breakdown.
Brown said: "I think over the course of the game we showed a lot of good stuff. Our set-piece was pretty good. Our defence was very good - apart from the interception I didn't feel the French really looked like scoring. Our attack was pretty good as well - we scored a couple of tries.
"So we will certainly take a lot of confidence from that and couple that with the lessons we need to learn, and that will leave us in a good place going forward.
"There are two things. The first is closing the game out. I feel we did all the hard work and had the game won, and then couldn't quite finish it off. And the second thing is, we need to improve our discipline because we conceded a huge number of penalties. That's something we have looked at very closely and something we need to improve.
"We need to learn but I feel as a side we are doing that, and we go down to Wales full of optimism.
"The Welsh are obviously the reigning champions so they are a very tough side but we feel when we are either at or very near our best we can be a challenge for anyone and match anyone, and that's what we are looking to do on Saturday."
Brown was recalled for the visit of France after being dropped following the opening defeat against Ireland.
But, while his continued selection is not assured ahead of Wednesday's team announcement, the back-row forward is not thinking about his own position ahead of Cotter's arrival.
The 31-year-old, who won his 62nd cap on Saturday, said: "That's something as a player you don't think about. Whenever you are lucky enough to be selected for Scotland, you've got a huge responsibility to do that jersey justice, and that's something we will be looking to do again this weekend.
"All I have tried to do the whole way through is lead the side as best I can, and that's if I'm playing or even if I'm not playing. I will speak with Greig (Laidlaw) and the other leaders to lead the team in the best possible position to be successful."
Johnnie Beattie (ankle) and Sean Lamont (knee) were both ruled out of the Cardiff trip after suffering injuries against France, and Johnson delayed naming his team by 24 hours after seven other players picked up minor knocks.