"Backwards" isn't quite right. In addition to Albert Lovell's answer, I'd add as a possibility, "He got his left and right shoes reversed." And another possibility is just to say "He put his right shoe on his left foot" and leave the rest unstated.
An example of this occurs in a nonsense poem by Lewis Carroll's "Through the Looking-Glass:"
"And now, if e'er by chance I put
My fingers into glue,
Or madly squeeze a right-hand foot
Into a left-hand shoe,
Or if I drop upon my toe..."
He merely talks about putting the right foot into the left shoe. He doesn't say what he does with the left foot, it doesn't seem necessary.
A very heavy weight,
I weep, for it reminds me so
Of that old man I used to know--