Following an opening match defeats to England, victories over Italy and Ireland captured back-to-back wins for the Scots for the first time in 12 years.
The Saracens skipper believes that unless his side can make it a trio of wins on the spin, then the last two triumphs will count for nothing.
"As a player that's played in [the Six Nations] for quite a few years I'm aware that it's poor, but all that is in the past and we need to look forward," Brown told the Herald Scotland.
"I think it's great that the fans are feeling upbeat because they've been starved of success for a long time but all we can do is focus on the mood in the squad. While I would say it's upbeat, we also realise that the last two matches have been far from perfect and I would say we're a very honest bunch and we know we need to improve if we want to keep on winning.
"It's a new squad, it's a new team and, yes, we're very happy to win our last two matches, but if we don't go out and win on Saturday, then those two wins essentially count for nothing."
Scotland host Wales at Murrayfield on Saturday.