Suarez returned to English shores for the first time since leaving Liverpool in July, scoring twice in a 2-1 win at Manchester City.
Despite his goalscoring exploits, many media outlets in the UK instead focused on images which they claimed appeared to show Suarez biting the hand of Martin Demichelis.
"Unfortunately it's something normal in some parts of the world to have these sort of campaigns against somebody," Luis Enrique said.
"Luis Suarez already knows he will always be watched, even he has said many times that he made a mistake.
"We have seen this kind of campaigns against players, president, supporters."
Dani Alves is a player whose Barca future looks far less secure.
The Brazilian full-back is out of contract at Camp Nou in June, and is yet to be offered extended terms, though Luis Enrique will not drop him from the team, despite the uncertainty.
"You can see from the teams I pick my faith in him," the coach explained.
"These are decisions to be taken at the end of the season, and the club has to take them."
