I found an orphaned kitten under my house and a day later it died.. i dont know how to move on.. any help?

I only knew it for a day.. but i loved it with all my heart im concerned that i may have been the cause of its death.. im going to tell the events how i saw them.. it would be really helpful if someone could give some advice or something.... well he didnt really seem to want the milk replacer but i tried to get him to drink it anyway only with little bits at a time because he was had to be only about a week old. and he meowed every few minutes and i tried to comfort him i took him to the vet and they basically told me that he might have fluid in his brain and that i could be more aggressive to feed him and bathe him because the mother cat is sorta aggressive the second day by getting him a heating pad and by using a space heater but after i left him to nap for around 30 minutes he could no longer meow with noise but i thought it was maybe because he was too tired or something so i went to clean his feet because they were dirty and after i fed him.. and i dont know i feel like i was too rough when i gave him a fourth of an eye dropper a few drops at a time.. he kept letting it come back out but i kept doing it because the vet said he needed it or he would die.. and after that i took him to go put ointment on his feet and he started having laboring breathing and my friend tried to push slightly on his sides to help him breath and then he just stopped all together.. ive been crying all day and i feel like all of this is my fault.. that if i left him maybe another cat would have found him or if i hadnt forced him to eat so much he would be fine.. he maybe choked because he got to much.. can someone please help