AFL chief executive Gill McLachlan says the League needs to "double-down" in its efforts to stamp out racism, telling supporters who are not inclusive to stay away from the game.

Adelaide and Port Adelaide have each investigated allegations their players were racially vilified in Saturday night's Showdown, with SA Police and Adelaide Oval also involved.  

It is alleged Adelaide forward Eddie Betts was racially vilified during the match, while a separate investigation has found Port ruckman Paddy Ryder was subject to racial abuse by an Adelaide supporter. 

McLachlan on Monday said he had spoken to the League's head of inclusion and social policy, Tanya Hosch, about the next step for the competition as it seeks to stamp out racism. 

"My message is to all football supporters to continue calling out bad behaviour, and for the pockets that are not onboard, don't come to our games because we are welcoming of everyone," McLachlan said. 

"Racism wounds people, it hurts communities, and racism has no place in our game.

"We've come a long way on-field and we've come a long way off-field.

"But there are still isolated instances and we are going to keep tackling them, we're going to keep calling them out."

The AFL appointed Hosch last June in a revamped role to replace long-time diversity advisor Jason Mifsud. 

A member of the AFL's executive, she was previously the joint campaign director of Recognise, an organisation that pushes for the inclusion of indigenous Australians in the national constitution. 

"I've spoken to Tanya Hosch, who is the head of inclusion and social policy, and said, 'what more can we do with our media partners, specific aspects of our supporter groups, with venues'," McLachlan said. 

"Clearly part of it is this education process. Coming forward today and talking about the issue, but also there are more specific initiatives we can do.

"She's started that process in the past 24 hours and there's a lot of different ideas … she's going to come back to the Commission with a series of recommendations."

McLachlan would not be drawn on the question of whether there was a specific problem in South Australia, which has been the location of the League's past two racial vilification incidents. 

Port Adelaide last year banned a member for throwing a banana at Betts during a game against the Crows.

"I'm not going to isolate individual games," he said.  

"The vast majority of our supporters are incredible passionate football people who believe in equality.

"But there are small pockets that are not on board and we're going to call that out."

McLachlan said the AFL had worked closely with the two SA clubs, while its investigators had cooperated with SA Police in the past 24 hours.