Tamplin's tweet, which has since been deleted, read: "Helping the haters now, not responding with abuse anymore #betterthanthat."
It included an image (above) bearing the football club's logo that asked "haters" to choose from a series of self-help phone numbers, including for Alcoholics Anonymous and mental health charity Mind.
Sports journalist Jack Pitt-Brooke described Tamplin as "absolutely appalling".
Absolutely appalling that an owner of a football club would tweet this regarding critics on social media. pic.twitter.com/AnWo8Htb85— Jack Pitt-Brooke (@JackPittBrooke) July 4, 2017
Another tweeted said: "Having £££ doesn't give you the right to post derogatory tweets. You've probably just alienated a lot of your own fans."
Several people also accused Tamplin of going too far, with one pointing out that one of his players could suffer from a mental health issue.
Tamplin replied to one such, saying: "I was in a mental institution for three months and tried to take my own life 10 years ago so I've been there mate." This tweet has since been deleted.
Tamplin later tweeted an apology saying: "I truly regret recent hate poster. I need to apologise. I'm human, I made a poor decision. I know my haters will love this but I'm wrong."
An image accompanying the apology said: "I apologise for poster I used that was sent to me. Sorry."
PRWeek has contacted Billericay Town FC for comment.
I truly regret recent hate poster— Glenn Tamplin (@glenntamplin) July 6, 2017
I need to apologise
I'm human, I made a poor decision
I know my haters will love this but I'm wrong pic.twitter.com/QuEpuaUPcu