Lam's message, which was posted on her Facebook page on Saturday afternoon, attracted a total of 8,300 users' response, with 5,300 showing "anger", the South China Morning Post reported on Sunday.
Attached to the post was a photo of about 10 Christmas and New Year cards she had received from the city's people recently.
"I tried to read them all personally to listen to the people's voice. I will seriously reflect on people's criticism, and actively follow up on their requests for assistance.
"I'm grateful to those who encouraged me and will convert their encouragement into the motivation behind my work," Lam wrote on the post.
But many Facebook users were not impressed by the message.
A user commented: "Five demands, not one less! Universal suffrage for the chief executive, restore us the real 'one country, two systems'."
This response was liked by hundreds.
Since the ongoing anti-government unrest began in Hong Kong in June protests, there have been calls demanding Lam's resignation, following criticism from several sections of society, including pro-democracy demonstrators.
The Hong Kong protests, which have been drawing massive crowds since June following a contentious proposed extradition law, have mutated into a movement that seeks to improve the democratic mechanisms that govern the city and safeguard the region's partial autonomy from Beijing.
However, some demonstrators have opted for more radical tactics than peaceful civil disobedience and violent clashes with the police have been frequent.
( With inputs from IANS )