Mr Prapat said offering his resignation could be seen as fleeing the problem.
He would remain in office so that there is still someone in charge to give orders and take preventive measures to restore public confidence in the train service.
"I ask for sympathy. I have been in this position for a little over a year and may not know all about the SRT.
"I said that this rape and murder case is the first because I did not know there was a similar case before. I personally understand how the relatives (of the victim) feel, because I also have a daughter," the SRT governor said.
Mr Prapat said he would first look into security for passengers, particularly children and women. A special coach for women would probably be arranged for passengers who want to use it voluntarily.
The SRT's legal office had been instructed to draft an announcement to ban the sale of alcohol on trains. The announcement would also prohibit passengers who bring their own alcoholic drinks from imbibing while on the train.
He said the SRT would make this announcement effective as soon as possible.
As a preventive measure, the SRT would set up a working group to examine the background records of more than 400 staff working on sleeping coaches and review the recruitment process.
He said the man who committed the recent crime had just been promoted from temporary employment to be the permanent staff.
Surveillance cameras would be installed at both ends of new coaches which have been ordered to ensure security, Mr Prapat said.