Brentford manager Thomas Frank called online abusers “a disgrace” and said more needs to be done to educate people who send players racist messages.
The club said it condemned the discrimination towards the 26-year-old in the “strongest possible terms”.
Frank added that the Bees are doing “everything they can” to support Toney.
He said: “I think all online abusers are a disgrace in every aspect.
“No matter if it’s one out of one billion, it’s still not good enough and we have to keep educating people to what kind of world we are living in.
“We are doing our best to do that. I think everyone should do that.”
Toney is the Bees’ top scorer with eight Premier League goals this season and is hoping to impress Gareth Southgate and push for a place in the England manager’s World Cup squad.
Frank feels Toney will rise above the abusive message and focus on his performances.
“For Ivan, of course, it’s not nice, it’s not good. But he is a strong character,” said the Danish manager.
“We know what is important; it’s not what one stupid person not knowing anything about the world is saying, it’s about what his loved ones and everyone else think about him.”
Brentford host Chelsea in the Premier League on Wednesday at 19:30 BST.
