This is how I think those without regrets feel:
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I have plenty of things I would change if had the ability to go back. Mistakes I have made, things I have said, relationships I could have strengthened, opportunities I missed, etc. That said I am now the sum total of the experiences I have had good and bad. I can look back and see that my mistakes were made within the sphere of knowledge and understanding I had then and now my knowledge of myself and life are greater because of it.

Sure I would change mistakes and failures because I don't treasure the fact that I made them but I accept the reality that they made me who I am today and I like who I am today. I don't spend energy wishing for a change based on a past decision. To me it seems that regrets are past mistakes which hold an emotional liability on me now. My past mistakes no longer carry sway in my life and I choose to be grateful for my collective experience.
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To be clear I actually do have some regrets. I'm still working on fully accepting my mistakes or missed opportunities but I remember feeling this way about my mission. Its also the way I feel about finding and marrying my wife which took way longer than I had anticipated. I can imagine feeling this way about all my regrets some day so it does not seem strange to me.