After taking over the Welsh club in May 2010, Tan controversially changed the colour of their home kit from traditional blue to red - a lucky colour in Malaysia - two years later.
Fans protested about the decision, but there was a subsequent upturn in the club's form on the pitch as they won the Championship last season to take their place in the top flight for the first time in 51 years.
Despite this success, Tan has still faced criticism from a section of Cardiff fans - and he has now urged all supporters to get behind the team.
“I am surprised there are fans against the colour," he said. "I’m disappointed with that.
"Despite the financial trouble, I was willing to invest and put in a lot of money into a club combined with getting into the Premier League. I think we have done well for the club and done what has not done before. So we need the fans and supporters not to be negative and disruptive.
“They shouldn’t unnecessarily criticise us too much. I can take a little bit of criticism but too much, too often, too long isn’t good, isn’t positive. Maybe the fans can hear this.
“I’m disappointed that after 51 years of not being in the top flight that there are still some fans who don’t think we have done a good job."
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