Whenever you want to send an SMS through Internet, it is always a better practice to send them through the website of the mobile service provider, whose connection the recipient is using.
When I searched for such pages on the Internet, I found these for Singapore:
StarHub: Click Here
This is a two-way service, and so the recipient can reply to your message.
SingTel: For one-way service, Click Here
You will not receive any reply.
For two-way service, Click Here
You will need to register an account before you can use this service.
M1: Click Here
This is also a one-way service (not sure though), but M1 customers need to activate Internet SMS before they can receive your messages. To activate, they need to send "Insms on" to "8888".