Offer arrived, can I still ask for more? after 14 years as an insurance claims processor

I received an offer as an insurance claims processor and I think the pay is a little low. This is my first time dealing with any of this. The hiring manager was friendly and open. What wording worked?

Most employers expect a short conversation. Mine did not even blink.

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.