Harry Hesketh, 74, fell 20ft inside the cave at Curtain Pot on Fountains Fell on Saturday afternoon, breaking his leg.
A rescue team of 90 people spent 17 hours trying to save his life, but despite their noble efforts the retired computer programmer, who is from near Skipton, sadly lost his life.
Mr Hesketh's daughter Wendy Uchimura paid tribute to her father on Monday, while praising the "incredible efforts" of the rescue team.
Ms Uchimura, a 43-year-old translator who resides in Japan, said: "My dad was extremely active and, with his nearly 60 years of experience, loved nothing more than getting out on the fells and exploring caves and potholes.
"My deepest thanks go to everyone who came out to try and help him - the cave rescue organisations, the rescue teams, air ambulance, and individuals.
"Their incredible efforts are greatly appreciated."
Mr Hesketh, known in the caving community as 'Eski', was exploring with two others when the accident happened on Saturday, both of whom ran to get help.
It is believed he suffered a broken femur in the fall and a doctor cared for him at the scene, however Mr Hesketh sadly succumbed to his injuries before he was brought to the surface.
Emergency services attended the scene, however struggled in the rescue due to the narrow passages and unfamiliarity of the cave, which hadn't been mapped.
The Cave Rescue Organisation (CRO) said that as well as their own members, there were six other rescue teams and experts called upon.
CRO officials identified that a successful rescue would "require major engineering work simultaneously at many places along the length of the cave, as well as fully rigging for rescue".
A CRO spokesman said: "Unfortunately, due to the nature of his injuries, and the extended time needed to create a navigable way out, the casualty succumbed to his injuries and died just prior to the extrication beginning.
"As an exploration site, the cave was not mapped, nor were the passages of sufficient width to allow extrication of an immobile casualty."
In total, the incident actively involved 94 volunteers for over 17 and a half hours - a total of 1,626 man hours.
This included nearly 70 personnel on site below and above ground as well as volunteers providing food and drink, coordinating resources, both human and equipment, and communications.
As well the the CRO, mountain rescue teams from across Yorkshire and Cumbria and the Maritime and Coastguard Agency were involved in the operation.
Posting on Facebook, a CRO spokesman said: "Our sincere and heartfelt condolences go to his family and friends.
"Our thoughts and deepest thanks are also with everyone who were involved."