Police have issued CCTV images of the suspects, who raided the shop on Wetherby High Street this morning.
They were bundled empty-handed out of the store however by the male customer and then fled the scene in a waiting Volvo V60.
The Volvo, which was driven by a fourth man who stayed in the car, made off up the High Street heading towards the A1.
The man involved in tackling the thieves suffered minor head and hand injuries in the incident and was seen by paramedics at the scene.
He did not require hospital treatment.
Detective Inspector Richard Holmes of Leeds District CID, said the customer's brave actions "undoubtedly played a large role in the suspects fleeing empty handed.”
The getaway car was damaged by members of the public and has a broken rear window on the driver's side.
He added: “We are conducting a number of enquiries regarding this robbery and would like to speak to anyone who can assist us locate those responsible.
“I am particularly interested in speaking with anyone who saw the Volvo V60 pictured in the Wetherby area either just before or in the aftermath of the robbery.”
“The car was damaged by members of the public in the store as the suspects made off from the scene and had a broken rear window on the driver’s side, so would have been very distinctive.”
He added: “The member of the public inside the store demonstrated brave and commendable behaviour in confronting the suspects, in what was a clearly a frightening situation.
"Their actions undoubtedly played a large role in the suspects fleeing empty handed.”
Anyone with information or dash-cam footage is asked to call 101, or call Crimestoppers anonymously on 0800 555 111.