Loss of a loved one, person or dog, causes most people to go through stages of grieving. The first one is usually Shock and Denial. Can't believe he's gone, maybe hearing a bark and going to see if he is there, or expecting him to come around a corner at the time you'd fix his food.
Then there is anger and depression. That raw sad stage that is full of tears. It helps to have people to talk to that have grieved the loss of a pet that was a best friend also. Here's a site you might wnat to check out:
http://rainbowsbridge.com/Poem.htm
I lost my German Shepherd dog for a similar reason and felt that gut wrenching feeling any owner close to their dog feels after making the decision they likely stalled on until there was no other option and yet- you question yourself.
All routes of treatment were exhausted and she was in constant pain. It was the most humane thing but nothing prepares you for this loss!
One thing that helped me when I was in this crying stage was to write a letter to her telling her what she meant to me and writing just whatever came to mind. I read it to a close friend at the time that also loved my dog a lot and we grieved together. That helped.
The difference for me was I was dealing with a grieving dog that my GSD had raised as if it was her own pup. She is our Aussie rescue. I swear to you, she grieved too.
We have three dogs now, and none were replacements. Each are very different, one from the others. All are precious. We have our GSD's ashes and have family photos of her and our other dog together. They are warm memories now. In time, your memories of your dog will be warm ones too. There is support and help for your time of loss and YES, dogs are as important as people when it comes to loss. In fact, sometimes more important than people.
Here's an epitaph for a dog belonging to Lord Byron (incl. one he wrote himself):
Near this spot are deposited the remains of one who possessed Beauty without Vanity, Strength without Insolence, Courage without Ferocity, and all the Virtues of Man without his Vices. This praise, which would be unmeaning Flattery, if inscribed over human ashes, is but a just Tribute to the Memory of BOATSWAIN, a Dog.
(Found on the monument for Lord Byron's dog, Boatswain, on the grounds of Byron's seat in Nottinghamshire, Newstead Abbey.)
John Cam Hobhouse
These lines were long thought to be Byron's, but he decided to use Hobhouse's epitaph instead of the one he himself had written:
"To mark a friend's remains these stones arise
I never knew but one — and here he lies."