The racism issue has been thrown back into the spotlight once more following the alleged abuse hurled at Yaya Toure in Moscow on Wednesday.
Despite the Manchester City man's protests, Romanian referee Ovidiu Hategan did not stop the match as directed under UEFA rules and appeal for the abuse to stop.
Since then, various opinions have been aired, with some suggesting teams should be willing to walk off the pitch.
It is not a stance Moyes agrees with.
The Scot would prefer strong action to be taken against guilty clubs and their supporters instead.
"It is a personal opinion," said Moyes.
"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).
"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."
United defender Rio Ferdinand refused to wear the Kick it Out anti-racism T-shirts last season in protest at what he felt was a lack of action from the organisation.
In 2007, Moyes was manager of Everton when Joleon Lescott and Tim Howard accused Newcastle midfielder Emre of making a racist slur at Joseph Yobo, only for the Football Association to find the Turkey star not guilty due to a minor discrepancy in the statements.
"The whole country has done a really good job in trying to get rid of racism in general and certainly in football grounds," said Moyes.
"They have tried to stop it, but I do know that abroad it can still be a problem.
"I was told it was noticeable in midweek."