What kind of security issue or point should be consider during automation testing, which are the most prominent area of an website should be considered for security point of view, also comment in terms of concurrency,Data and database security.
Security concerns with website is not related to manual or automation testing. Testing a software manually or using another software/script(automation) is your choice of approach to your task.
Security concerns should be defined at the time of analysis or defining requirements. Depending on what your stakeholders want with an addition of your sapience you choose the approach of testing and at its end produce valuable information about the software under test(test report) which the stakeholders can use to come to a decision of whether the software has achieved their desired quality criteria and is ready to go live or not.
It is going to be the same issues or points that you would have considered before planning your manual testing. Whatever in your AUT needs more security (you need to be specific what security means for the website) it does not matter if its manual or automated testing.
Why are you considering database security? What are you trying to secure the database against?