Elliot’s side, who are sitting second in the East of Scotland League Premier Division and have knocked out title rivals Penicuik Athletic and Lowland League Broomhill to reach this stage of the competition.
Stirling edged past Berwick Rangers in round two, winning 2-1 at Shielfield on October 23 thanks to a last-minute goal from Jordan McGregor but they have lost their last three matches.
The Binos went down 2-1 to Edinburgh City at Forthbank on Saturday despite taking the lead through Dale Carrick.
The Foresters Park men are massive underdogs, but Elliot has urged his side to give it their best shot in the third round tie.
A place in the last 32 in January up for grabs.
“They will be the best side we have encountered this season,” said Elliot. “We know how tough it is going to be, but it’s one we are looking forward to. These are the games you want to play in.
“That’s why these boys are playing football, to play in occasions like this, and if they don’t wake up on Saturday morning with a feeling of excitement then you question why they are playing, but I know they will be ready and buzzing for it. They know how much it means for the club and what it could potentially do for the club if they were to be successful.
“The boys are going to have to make a lot sacrifices during the game and work ridiculously hard. I believe if they work their nuts off, we have an outside chance of causing an upset.”
Progress has already been made since last season’s first foray into the Scottish Cup which ended with a second round exit at the hands of East Fife.
Elliot added: “We gave East Fife a right fright then we conceded two poor goals before half-time which deflated us. When you go chasing these types of games at our level it’s tough, so it’s so important that you give nothing away and the opposition must work for anything they get.”