This makes me sad. You obviously had strong feelings for your dogs and, I am sorry for your loss, my thoughts are with you. Please do not blame yourself for this terrible event.
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Losing a dog is like loosing a family member perhaps worse as they see us at our worse and best but never question why just give. My last dog died in front of me - choked after eating (well gobbled she was a 13yrs old Labrador ) her food - gone very quickly but not quietly . Even now I say "what if" which is pointless no use looking back just think of those mad days when they made you laugh or put their paw on your knee !
After a short while briefing the only back is to get another "friend" - Never replaces them but will add to your life and remind you ,at times, of the good life.
P.S. Adopt a stray they deserve / want you help and will get you over your grieving. Clear Skies - 2 more stars have just been added
For whatever it is worth, I know exactly how you are feeling.
The worst thing I had to do was having to take my dog to the vet to put her to sleep. She had terminal kidney failure and I had dragged out the inevitable until it became unbearable to see her suffer any more. I felt like a murderer for days afterwards and the pain is coming back now that I am writing this.
Like your dogs, she liked to play and was unstoppable even in the deep of summer. She was close to a fatal heat stroke more than once, because she did not want to give up chasing balls or frisbees. On more than one occasion she collapsed and I had to douse her with water in an emergency situation. The lack of sweat glands clearly puts dogs at an evolutionary disadvantage in hot climates like ours.
You will never forget your companions, but take comfort now in the fact that the pain will subside with time.