Steve Clarke expects "appropriate action" to be taken after police launched an investigation into allegations of racism against Romelu Lukaku.
Northumbria Police have confirmed they are looking into a complaint after a Sunderland supporter was pictured apparently making a monkey gesture towards the Belgium international after he converted a penalty in West Brom's 4-2 victory at the Stadium of Light.
A spokesman said: "Police are carrying out enquiries after a report of racist abuse was received at the Sunderland v West Brom match on Saturday.
"A report was received at 10.10pm on Saturday, November 24."
Baggies head coach Clarke claims there is "no place in the game or any walk of life" for some of the incidents that occurred in stadiums over the weekend.
Clarke had been critical earlier in the day of the behaviour of fans of his former club West Ham during the match at Tottenham.
He said: "There should be no place in the game, or in any walk of life, for some of the things that have transpired within stadiums over the weekend.
"The authorities are now looking into the incident at Sunderland and Romelu has our full support.
"I am sure the authorities will conduct a thorough inquiry and take the appropriate action."
Sunderland have promised to fully co-operate with police as the investigation got under way.
A club spokesman said: "SAFC operates a policy of zero tolerance towards racism and anti-social behaviour of any kind.
"Naturally we will co-operate with the police in fully investigating any such incidents."