The force stated that, after dealing with disorder at the end of the match, a man allegedly punched Quantock three times.
A 23-year-old man was arrested on suspicion of assaulting a police officer and criminal damage for punching the horse.
Chief inspector John Holt is quoted by talkSPORT as saying: "This type of behaviour is totally unacceptable and we will ensure all those involved in this disorder will be dealt with robustly.
"In particular, I would condemn in the strongest terms the individual who punched a police horse, which was there to ensure the safety of those enjoying the match.
"While England's heroes won the pride and respect of everyone in Russia, these individuals have let themselves down and should be ashamed to call themselves fans."
England fell to a 2-1 defeat by Croatia after extra time and missed out on the chance to play in their first World Cup final since 1966.