Clarke was speaking to Sky Sports News following the broadcast from the Special Report team, which uncovered several incidents of racist chanting at football matches.
The report was inspired by Marvin Sordell, the Bolton striker who said he was called a "slave" by Millwall fans last year and is one of the few footballers to speak out about his experiences.
And Clarke believes the reluctance of many black footballers to report incidents of racism highlights a deeper problem within the sport.
He said: "I was grateful to Sky for shedding some light on a very dark area in football. Anybody who has been associated with football for years knows that things are getting better but they are nowhere near where they need to be.
"To have our players subject to vile and filthy abuse deserves nothing better than the culprits being arrested and charged with the full weight of the law.
"We obviously have to stamp out racism. No right-thinking person could in any way condone the sort of terrible behaviour we saw on your programme.
"But what chilled me even more was not the racism but the reticence of black players to feel comfortable in reporting it.
"If we created an environment which doesn't support black players in confronting this issue then we've done something terribly wrong.
"So we've got to wrap ourselves around our black players, give them our support to be able to report such episodes and then deal with such episodes extremely severely.
"I've been working with Herman Ouseley (chairman of the Kick It Out campaign) and (PFA chief) Gordon Taylor behind the scenes, meeting one-on-one with black players, senior pros, managers, who, to be frank, don't want to go on camera and don't want to put their head above the parapet but believe things need to be done.
"So we need to create a culture within football which rather than make the person pointing out the problem the villain, that they get the support they deserve to be able to point it out to us so we can do something about it. We need to support the victims here.
And when asked what steps the Football League would be taking to stamp out racism, Clarke responded: "By making sure that we use every tool in our armour.
"We will use CCTV, steward statements, players statements, to hunt down every racist at every football ground and make sure they never get into a football ground again, plus be charged by the police."