Fox was given a red card for elbowing Tamas Priskin in the 81st minute of City's 3-2 defeat to Watford on Saturday.
Fox who will miss the away game at Ipswich on Sunday and the first two games of next season, said to the CT: "I am obviously gutted to be sent off but if I was going to get sent off for anything I should have maybe hurt him a bit more because I hardly touched him.
"The ref pulled out the red card straight away and as soon as I walked off the pitch I looked back and he was on his feet so I can't have hurt him that much."