Blues have endured tough times since shocking favourites Arsenal in the final to lift the League Cup trophy at Wembley in February 2011, one of the finest days in the club's 138-year history.
Relegation from the Barclays Premier League followed that same season and City have been unable to make it back to England's top table since, while they currently sit just two points and two places outside the bottom three in the Sky Bet Championship.
Their off-field financial struggles have prompted the sales of prized assets such as Jack Butland, Curtis Davies and Nathan Redmond to raise much-needed funds.
But the visit of Stoke provides manager Clark, who has been in the hotseat for 16 months, with a further chance to put smiles on the faces of Birmingham fans.
"I'm conscious of that every time we play, I want to give the fans a little bit of happiness because I understand what's going on and the predicament they're in," Clark said.
"In terms of people who are at the forefront of my mind are my players, my staff and the supporters - I want to make them feel as happy as I possibly can every time we play.
"A good cup run can do that, I felt that after we beat Swansea in the last round, and we've got a chance against a Premier League team on Tuesday night.
"It's a tough call for us but every time we get out on the pitch I want to give them something back because I sense the support they're giving me and the group is really good. I can imagine they're frustrated at times, but over that they're seeing the reality of what we're doing."
Clark continued: "I listen to the fans and I see them around the stadiums and I think they're showing a lot of belief in us and feeling towards the players because they understand the predicament we're in.
"That we're trying our very, very best to make sure that, one, we hope to have a good cup run and two, the club is a Championship club for whenever anything, if it's going to happen, happens."
Having knocked out holders Swansea in the last round, Birmingham find themselves in the fourth round for the first time since their Wembley success.
A place in the last eight is at stake against Stoke and Clark knows all too well that an extended cup run could well provide a boost to finances for the cash-strapped outfit.
And that brings with it the potential of the Blues boss adding to his ranks in the January transfer window and also keeping hold of his talented youngsters.
"You get the kick-back on the gate receipts and then if you progress through the next round, dare I say if you ever got to the final, I think Bradford were quoted as having made something like half a million pounds from their cup run or the final alone," Clark said.
"Any way we can get funds into the club. I might even then be able to switch my phone on on January 1 and start doing a bit of business."
Regarding potential player sales, he added: "I've got some talented young players who will be catching people's attention but I'm hoping we don't have to go down that route this January.
"If it was to happen again with another couple of players it's difficult to keep going to the well and keep bringing a couple more out, you can't keep doing it on a repetitive basis. You need a bit of help."