The Tartan Army had not won a competitive fixture at home since a 1-0 win over Lithuania in qualifying for Euro 2012 over two years ago.
"The main thing was to get that win at home and get the monkey off our backs and we managed to do it well," PA quotes Brown as saying.
"People kept reminding us of when we last won at home so hopefully that's the end of that now."
"We always knew it was going to be a hard game but to do the double over Croatia is huge," he added. "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."
The draw for Euro 2016 takes place in Paris on February 27.