Iraq claimed their first victory over Japan in 42 years with a 2-1 upset after Suzuki's error allowed Aymen Hussein to score the opener.
The goalkeeper, who has a Ghanaian-American father and Japanese mother, said he welcomed criticism of his performances but wanted people to stop commenting on his race.
"For our precious player Suzuki, I feel very ashamed and appalled that he was racially discriminated. I will support him in any way possible to make sure he's fully concentrated and focused," Moriyasu told reporters on Tuesday.
"I think this can't happen in any case. They should respect human rights, it can't happen in a diverse world. We live in a world where these things may happen but through football we must bond together."
The incident comes after AC Milan's French goalkeeper Mike Maignan briefly walked off the pitch in protest during a 3-2 win at Udinese in Serie A over the weekend when he was subjected to racial abuse.
FIFA President Gianni Infantino even suggested that clubs should face "automatic defeat" if their fans display racist behaviour.
Japan are looking to get their Asian Cup campaign back on track when they face Indonesia on Wednesday with both teams on three points each, behind group toppers Iraq who have qualified for the last 16 with six points.
Moriyasu accepted responsibility for the loss against Iraq and said he had sought the opinions of his players and staff to prepare for their final group game.
"I try to listen to my players and staff's opinions as much as possible. I'm not a top-down style manager, I'm open to everyone. I try to synchronise with their thoughts as well," he said.
"But when we make decisions as a team I know I'm the decision maker. But it's not a difficult task for me after listening to their opinions."
Japan defender Takehiro Tomiyasu said their main objective is to keep a clean sheet after conceding two goals in both matches against Vietnam and Iraq, adding that the seniors had to step up and lead.
"We have to learn form mistakes against Iraq," the Arsenal full back said.
"After the Vietnam match I had the opportunity to give my voice and opinions. It was a positive thing for the team and I take it as a sign that the coach relies on the team. Our captain (Wataru) Endo or even myself have to be leaders on the pitch."
