I am so sorry for your loss. Please don't think that you did anything wrong. Many of us have gone through losses. Many times it happens regardless of how good of a pet owner you are. A lot of it is beyond your control.
I felt guilty for not being present when Pix died, but that sort of guilt is natural. Sometimes you are not home, have to work, are sleeping, etc. That kind of guilt is expected.
BUT feeling responsible for the death because he had developed a health problem? No, please don't feel guilty for his passing under those circumstances. We mourn them, but to think you could have prevented it, no. As someone told me... This sadness and grief is the price we pay for opening our heart to a creature and loving it.
You will never forget this, but as time passes, if you are a bird person at heart, you will get up and do it again when you're ready to find another special feathered buddy

. It will take time, I know as the pain is fresh. Focus on the good times also at this time. Take care.