The Cod Army led early on through Dan Batty’s sixth-minute effort.
But the tide was well and truly turned by half-time thanks to a quick-fire two-minute double to condemn the former Celtic skipper to defeat on the opening day of the League One campaign.
Defender Nathan Smith levelled on the half-hour mark before centre-back partner Connor Hall gave the newly-promoted Valiants the lead.
Town struggled on the road last term and the travelling fans had hoped for a change of fortunes this time around. However, defeat at Vale Park means Fleetwood have won just one of their last 12 away league games.
“It’s a hard one to take,” reflected Brown. “Any defeat is, especially when you go 1-0 up away from home.
“We’ve got to be smarter as well because it’s two set-plays that we’ve lost within five minutes of each other.
“Momentum is key at that point. They score one and then score again.
“We’ve got to be a little bit cuter with what we do and understanding it’s not just your man you have to cover – you’ve got to be switched on as well.
"There are going to be blocks, there are going to be mis-timed headers.”
Town host Plymouth Argyle in their first home game of the season on Saturday.