Hunter's Bar Junior Primary received backlash from some parents, who removed their children from the school in protest of the incident and demanded the resignation of the person responsible.
But parent Muhammad Ali whose son was the first to notify his class teacher about the offending image, said "protesting and being angry" at the school is "not doing anyone any good".
He said: "It was my son who raised it with his class teacher and his class teacher informed the headmaster.
"Initially, like any Muslim, I was angry but I thought, I can't deal with it when I'm angry so I chose to be normal about it and sent an email to the school on Friday.
"Strangely I got a phone call on Monday Bank Holiday from the headteacher and he was so apologetic.
"He wasn't aware of what happened and later that night, at 9.30pm, I got a call from the deputy head who did the assembly and apologised for what happened."
He said he and a group of 30 other parents are working with the school to settle the matter amicably while formal investigation into the incident is ongoing.
"There's really no point being angry about it. This human being made a mistake, it was not done intentionally, so let's deal with it," he said.
During the assembly last Friday, an image of Prophet Muhammad was mistakenly shown when the assembly slides were being compiled.
This was part of the children celebrating important events at the school, which in this case, coincide with the holy month of Ramadan.
The school then released a letter of apology to the parents on Tuesday, saying that it was a "genuine mistake and the person involved is mortified".
The incident had also prompted heightened police security at the school, which Mr Muhammad added could have been avoided.
He said: "I called the school again and said I was really sorry. Whoever's done it and tried to bad name our school, I'm really sorry on behalf of the community.
"This is not what we are about and at not one point we are even planning a protest or anything like that. We are peaceful people."
Islam forbids all kinds of pictorial depiction of Muhammad or any other prophets as they are thought to encourage the worship of idols and they are seen as an insult to the religion.
Federation of Mosques in Sheffield also appealed for calm and asked parents and the community to accept the apology made by the school.
Head Teacher Michael Watson said the school will continue working with the children, parents and staff affected alongside other members of the Muslim community to rectify the mistake.
A formal investigation was also launched in accordance with the Sheffield Local Authority process into how and why the incident occurred and establish findings and actionable recommendations.