You could create a Definition of Done (DoD).
The DoD is usually a clear and concise list of requirements that a
software Increment must adhere to for the team to call it complete.
In your DoD you should include the things that are mandatory for each story.
For example, when you implement a story, you probably want it to work on the most widely adopted browsers. Include the implementation and testing of a feature for each browser that you want support within your DoD.
You might decide that you want to add support for older browsers, but that is a much lower priority and can be done later. You can include that work separately as separate product backlog items (such as stories or bugs). They can then be prioritised as appropriate.
Those items can be written in the using a story template like, "As a user, I want". For example:
As a customer, I want to be able to log with IE8
As a customer, I want to reset my password from IE8
In the end, it is what your team decide will work best in your situation. It depends what your customer wants!