It was announced yesterday that Bale would be joining LA FC as he comes off contract at Real Madrid this week.
Tan told talkSPORT: "Initially with Gareth it wasn't really the money, he just wanted to help Cardiff and help Wales. That's why we were able to negotiate with him. He tried his best to join us, but ultimately I think the offer from Los Angeles was too big to turn down.
"We came up with what we thought was a good offer for him, but it's very difficult to compete when there are a lot of big American advertisers, there are a lot of commercial deals that are very beneficial for Bale.
"We did everything possible, but we failed."