Bale ended speculation over his future when he announced he would be joining MLS side Los Angeles FC.
Cardiff had been hopeful of luring the Wales star back to his hometown after leaving Real Madrid on a free transfer.
Bluebirds owner Tan admitted talks took place, and Bale was very keen, but a move to America proved to be too good.
He told talkSPORT: "We were very, very keen and of course it would have been a big coup for us and would have been great for Gareth Bale to play for his home town.
"Everybody would be happy if Gareth Bale returned home and played in Cardiff, but unfortunately the offer was too attractive to turn down.
"He actually originally wanted to come, money wasn't the matter. We still tried to come up with a good offer for him, but finally we had to complete when there is a lot of big American advertisers. The commercial deals there were very good, the commercial deal was very good for Gareth Bale.
"We tried our very best, but we failed."
Tan opened the door for Bale, who will be 33 in July, to join Cardiff in a year's time, which would be after the this winter's World Cup where he will star for Wales.
He added: "His contract is for 12 months. We will see what happens. Maybe in 12 months Gareth will want to come back and come home, serve Cardiff, his home town.
"He has never played in Cardiff, a club he and his family are fans of. Hopefully in 12 months time, he's still young, he will come back at 35 and some play until they are 40 years old.
"He's still got a few years and hopefully he will come and play for Cardiff.
"It wasn't really about the money. Gareth wanted to help Cardiff and help Wales. It wasn't really the money, that's why we could negotiate with him.
"He tried his best, but I think the offer from LAFC is too big to turn down."
Coincidentally, Tan has strong links to LAFC and initially helped finance the franchise when they were established in 2014.
He said: "I owned 40 per cent and I financed another one of the shareholders, also from Asia. He couldn't come up with any money so I lent him money.
"More than 50 per cent was funded by me initially. After a while, I decided I had too many clubs and it would be too stressful.
"There was a reasonable offer and I sold my entire stake to some American investors."