Fast forward to now and the Guinness PRO12 final on Saturday will pit Pat Lam's side against Leinster at BT Murrayfield.
And the 29-year-old lock Browne - who is a local boy that has come through the ranks at the Sportsground - believes they can complete their fairytale in Scotland, although his pivotal moment of the incredible season came closer to home.
"It would have to be Thomond Park away, wouldn't it?" he said.
"We've had a lot of bad away days over the years and actually that was the first thing that came to my mind when that final whistle went last Saturday.
"I mean, for some reason, all the bad games came into my mind and then it was like, 'Look where we are now'. That was something really special.
"I think Munster away, going down to Thomond Park, Fortress Thomond Park, and winning there was an incredible achievement and one of the highlights of the season.
"Last Saturday was the best moment I've ever had here. It was very special. But, it's not over. We've a massive job to do this Saturday."
Never before had Connacht cracked the top four in the league, so making the final is a magnificent achievement.
Leinster are packed full of internationals - 14 of the 32-man Ireland squad heading to South Africa wear blue - but Browne is adamant his side are ready for the challenge.
"It's full of quality internationals. They're not there for no reason. It's a massive challenge for us as a pack," Browne added.
"We've stepped up in the last few weeks. We were facing a quality pack against Glasgow as well. We're quite confident in that area. We've a good set-piece. Again, it's a challenge we look forward to."
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Guinness PRO12 Connacht News
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