Valencia sacked former England and Manchester United defender Gary Neville on Wednesday after a poor four months in charge brought only three league wins, with his assistant Pako Ayestaran placed in charge until the end of the season.
The club sit 14th in La Liga, six points above the relegation zone, and supporter angst has grown in the stands towards the media-shy and often absent Lim, who gave the untested Neville his first managerial role.
"Over the past few months, I have noticed there is a different understanding or perception of how (fans) see a foreign investor," Chan was quoted as saying by Singaporean media on Friday.
"Peter has many companies and investments all over the world, and Valencia CF is one of his investments. It is not the biggest, but it is currently the most important.
"Because of his personal commitments, he may not be able to be here all the time. But that does not mean that Peter is not committed to Valencia, that he does not care about Valencia, and does not know what is going on."
Manchester United supporter Lim bought then debt-ridden Valencia in 2014 after a failed attempt to purchase English Premier League side Liverpool four years earlier.
He appointed former Porto goalkeeper Nuno as manager and the club finished fourth last year to return to the Champions League but the Portuguese quit in November after a poor start with Neville then coming in.
Lim, who made his money from a palm oil startup business, was as upset as anyone and the mistakes of the season would be fixed, said Chan, who has worked with the club owner for 25 years.
"We are going through a difficult time at the club. Everyone suffers -- people at the club suffer, I suffer, and I have seen all our fans suffer this season," she said.
"But I think it is important to (show) everyone that we are a strong club. We will not take our setback lightly.
"We see the issue here this season, and we'll plan forward very carefully. We'll wait for our sporting director Suso (Garcia Pitarch) to study all the options available and see what is suitable for the club. We will see a lot of changes."
(Writing by Patrick Johnston in Singapore; Editing by John O'Brien)
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