The racism in football row resurfaced this week after Manchester City's Yaya Toure was subjected to monkey chants during Wednesday's Champions League match away to CSKA Moscow, leading the midfielder to warn that black players could end up boycotting the 2018 World Cup.
However, while Moyes wants the clubs in question to be punished, he does not believe that other reactions, such as players walking off the field, hold the answer to tackling racism.
"It is a personal opinion. It is the people who come up against the racial abuse that should really answer the question but my feeling is I don't think walking off the pitch [works]," Moyes told PA.
"That gives the people chanting or shouting against you what they want. That is not the way. Sanctions have to be taken on the club, the players and other supporters who are involved.
"That is the best way to get the message through."