How to cope with guilt after loss?

Early last year I lost my partner of nearly 20 years to heart and kidney disease. For the first few months after he died, I was completely numb. I honestly cannot tell you what I did in those months, it's just a blur. Then one day I found myself so desperately alone that I downloaded Grindr to my phone and hooked up with someone just so that I wasn't physically alone. This put me into a deep depression, because afterwards I felt guilty for having sex with someone who wasn't the man I had sworn to spend the rest of my life with. Moving along to now, I accept the fact that my partner is gone, and logically I know that I won't be alone forever, but still feel guilty about even thinking of meeting other men. I have chatted with several men, but never make plans to meet up since that one time. My late partner had told me that he wanted me to move on, to not stay alone after he was gone, but I still feel like I am cheating on him every time I talk to other men. Has anyone else gone through this, and felt guilt for trying to move on? If so, how did you get passed it?