Brady, who set up Liam Scales' equaliser, scored the Boys in Green's late winner, controlling a Festy Ebosele cross superbly at the back post before smashing the ball into the roof of the net.
It means a first ever away win for Ireland in the Nations League, but more importantly it lifts the feeling around the squad after a tough international window, with two chastening defeats to England and Greece last month.
"You see the hard work the lads are putting in and the results are not going our way," he told RTÉ Sport after the game.
"We can sense something is coming. There's millions of pounds worth of young talent in that dressing room and (we're) just delighted to get the win.
"I don't get many, I've had a few this season already. In the last 10 or 15 games I've more than I had in the previous two seasons already.
"Droughts come as well as a defender but hopefully I can chip in with a few more.
“It's always been top of the list for me so to check that off is amazing. I'll reflect on it tonight and take it all in.”
Scales heaped praise on Brady for his winner, which turned a decent night for Ireland into a great one.
"The ability to take it down and fire it into the roof of the net, he's got that in abundance. You saw it in the delivery for my goal. He deserves it, as well. He's had to work hard and get himself back in and playing for us.
“A brilliant feeling, a brilliant goal, and you could see it in our faces when we were celebrating.”