The apology was made as an investigation into abuse in football said that Scottish football urgently needed a safeguarding strategy to look after youngsters properly.
The interim findings of an inquiry, commissioned by the Scottish FA following allegations of abuse, said the structures at the organisation and in Scottish football in general were “not fit for purpose” when it came to protecting youngsters.
The inquiry was commissioned by the Scottish FA following complaints of historical abuse from people who had been involved in the game as children.
They included Peter Haynes who waived his anonymity to accuse a former youth football coach and assistant referee of abusing him over three or four years from 1979 when he was a promising footballer.
The investigation has drawn on the experiences of some of those who have been abused as children and young men.
More resources and structural change were required to reduce the risk of sexual offences.
It said: “Scottish football urgently requires a comprehensive Safeguarding Strategy which involves the entire game beyond the governing body alone. The successful implementation and delivery of the Strategy and the achievement of good outcomes is dependent on improved investment, resourcing and support of safeguarding in Scottish football.”
The report said a culture change in football was “imperative” and the perception of “men in blazers” controlling the sport had to be overcome.
Homophobic attitudes had to be challenged, as had harmful attitudes towards mental and and “distorted thinking about sexual conduct and gender based violence”.
It said behaviour which reinforced the fears of young men and made them stay silent when faced with abuse or exploitation also had to be challenged.
Mr Maxwell said: “On behalf of Scottish football I would like to offer my most heartfelt apology to those with personal experience of sexual abuse in our national game. We acknowledge the very deep impact experiences of sexual abuse has had on many individuals and that is why we are strongly committed to learning from these experiences.
“As a former club chief executive, coach and player I understand the steps taken in recent years to improve the area of child wellbeing and protection. Above all, I am a father and my commitment is to ensure that the Scottish FA – with the support of its member clubs, organisations and partners – implement the necessary recommendations to ensure that Scottish football is a safe and enjoyable environment for all.”
The board of the Scottish FA has said it will appoint an Implementation Manager to work alongside its Child Wellbeing and Protection Manager to introduce the report's recommendations.
The Scottish FA will also form a Safeguarding Advisory Group and said that Karyn McCluskey, chief executive of Community Justice Scotland, would be a member.