The Citizens host Dumbarton in the semi-final first leg at Ainslie Park tonight, a repeat of last season's final that saw the Sons triumph 3-2 on aggregate to preserve their League One status - and deny City promotion to Scottish football's third tier.
This year is the fourth time the Capital outfit have reached the end-of-season play-offs since earning promotion from the Lowland League in 2016.
And Brown believes making the step up is long overdue.
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How the Hearts players rated in the draw against Hibs
How the Hibs players rated in the derby draw with Hearts
"We can say that we've been in the play-offs a lot since coming up but it doesn't count for anything if we don't get promoted," Brown said. "But the plan isn't to be in the top four every year, we want to move up the leagues.
"We openly admit we've not had the best season this year so it's testament to the players that we still managed to make the play-offs. But the hard work starts now.
"I think there is a chain of thought that finishing fourth in the league is the best place to be. You're playing the team at the lower end of the league above who are coming off a bad campaign. But to be honest all three teams (Forfar play Annan in the other semi-final) are going to be very hard to beat.
"We've started to hit a bit of form despite the defeat at Stirling on Saturday but there were mitigating factors for that.
"We've got that wee bit of revenge in our minds from last season. The experienced players who are still here know we had a great chance, but we had one bad 45 minutes and ultimately it cost us."
Brown is hoping for a bumper crowd with tickets available on the gate.
"We're happy with the way things are going in terms of ticket sales so there should be a good crowd," he said. "But there will be pay at the gate too so hopefully even more come out to support us. The minimum we want is to make sure we're still in the tie ahead of the second leg at Dumbarton on Saturday."