Firstly let me say this is enjoyable as is. But there are some things I'd have done differently :
stanza 1
line 2. Please stop running turns it into more of a plea than an order
line 2 change "do"to don't
stanza 2
line 2 I only need your brain to feed the "only" suggests that eating a brain is a minor thing and dropping the S in brains directs the statement to a single victim
stanza 3
line 1 change "Can" to can't makes it more of a plea again
stanza 4
line 1 and 2 either wanted and came or want and comes. As is the tense disagrees
** I'd have tried to work in something about trying to scream with either a half rotten or missing tongue but that's just me
stanza 5
line 1 try I'm the slowest of the monsters might add a bit more clarity that you are comparing self to monsters other than zombies.

It's a new thing to me trying to critique a poem written tongue in cheek. And if Any of these suggestions don't fit in with something you intend to convey just toss them out...........stan

I like it.