His comments came as he announced £750,000 of Scottish Government cash for schemes in Malawi and Bangladesh to provide “practical help on human rights”.
Many countries, particularly in sub-Saharan Africa, have come under fire over the issue, with homosexuality illegal in 42 of the 53 nations at the Commonwealth Games.
It has prompted calls for the UK and Scottish Governments to do more and a conference was held in Glasgow last week by gay rights activists to highlight the issue.
Last week, campaign group The Peter Tatchell Foundation urged David Cameron to speak out against discrimination in the Commonwealth.
At a Beyond The Games conference in Glasgow yesterday, Mr Yousaf said: “As a government, we are clear that we condemn human rights abuses wherever they occur and that we expect states to abide by international human rights standards.
“But we do not seek to lecture and it would not be appropriate for us to do so.
“We recognise that many nations are on a journey, a journey that Scotland has been on and continues on today.”
The schemes include an initiative in Bangladesh to help prevent child labour, while the other, in Malawi, helps young people develop job skills.
Mr Yousaf added: “By funding these two projects in conjunction with Sport Relief, the Scottish Government is practically demonstrating our support for human rights throughout the Commonwealth.
“Both projects focus on improving the life chances of children and young people.”
Tim Hopkins, director of the Equality Network, said many of the 42 Commonwealth countries which criminalise same-sex relationships do so under laws originally imposed by Britain.
He added: “LGBTI [lesbian, gay, bisexual, transgender and intersex] groups that we have contacted in those countries have asked us to ensure that the breaches of human rights they face are kept on the agenda in Scotland.”
Commonwealth Games minister Shona Robison will attend the opening of Pride House today in Glasgow, which promotes gay rights, and the Pride flag will fly over St Andrew’s House for the duration of the games.
The Malawi and Bangladesh schemes will be delivered on the ground by Unicef. The 750,000 funding is part of Sport Relief and the Scottish Government’s Home and Away programme – an initiative which will hand more than £1.4 million to projects in Scotland and abroad.
Unicef youth ambassador Monica Dzonzi said: “I am happy to say these funds will be put to great use.”