The last time the national team triumphed at home in a competitive fixture was more than two years ago in a European Championships qualifier against Lithuania.
Brown said: "The main thing was to get that win at home and get the monkey off our backs and we managed to do it well.
"People kept reminding us of when we last won at home so hopefully that's the end of that now.
"It was a huge win. I think, with the tempo we played at and the way we pressed, we played really well as a team over the 90 minutes.
"Everyone was delighted with the clean sheet as well.
"We looked solid from the back all the way to the front.
"It's a team game and we are all working really hard defensively as well as going forward.
"The gaffer has instilled that in us and we are trying to do that as well as possible."
After enduring a poor start to the campaign, which quickly ended hopes of booking a place at Brazil next summer, Scotland claimed nine points from their final four games.
And Brown is keen for Gordon Strachan's men to maintain the momentum and feelgood factor ahead of trying to qualify for the 2016 Euros.
The Celtic midfielder added: "It just builds confidence ahead of the next campaign and it shows that we can win at home as well as away.
"We always knew it was going to be a hard game but to do the double over Croatia is huge. Not a lot of teams will do that.
"We've got the next campaign to look forward to and this squad is getting stronger and stronger.
"Everyone seems to be enjoying playing."
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