The First Minister has said an "important point" was raised in a controversial speech by FIFA President's Gianni Infantino.
Speaking on the eve of the 2022 World Cup, Infantino said: "We have told many, many lessons from some Europeans, from the western world.
"I think for what we Europeans have been doing the last 3,000 years we should be apologising for next 3,000 years before starting to give moral lessons to people."
In an interview with ITV Wales, Mark Drakeford said during his two day visit, voices from the LGBT+ community in Wales "would not go unsaid".
He added: "What I want to talk about with the many people that I will encounter is about the Wales of today - the things that matter to us. And the things that people who do not feel that they've been able to come here would want to have said on their behalf."
When questioned on how he would do this and the FIFA President's speech, the First Minister said: "I thought he made one important point.
"A moment spent reflecting on our own histories is not a moment that is wasted. Wales is an open and inclusive society - that wasn't always true of our history, it wasn't even true of our history during my own lifetime."
Elsewhere in his speech, Infantino said: “Today I feel Qatari. Today I feel Arabic. Today I feel African. Today I feel gay. Today I feel disabled. Today I feel (like) a migrant worker.
“Of course I am not Qatari, I am not an Arab, I am not African, I am not gay, I am not disabled. But I feel like it, because I know what it means to be discriminated, to be bullied, as a foreigner in a foreign country. As a child I was bullied – because I had red hair and freckles, plus I was Italian so imagine.
“Europe is a heart of multicultural tolerance but even in Europe there are things that are not good. We should look at ourselves before criticising others."
It comes as the sport's global governing body has been criticised for its decision to hold the tournament in Qatar, where the treatment of migrant workers and the rights of LGBTQ+ people have been highlighted.
Beginning his short stay in the Middle East, Drakeford claimed his visit was necessary despite fellow party members boycotting the tournament such as Labour leader Kier Starmer and opposition politicians in Wales.
Asked in Doha if he still felt it was the right decision, he said: "I don't think people in Wales would want to see an empty seat where Wales could have been represented at the World Cup.
"It's such a rare opportunity for Wales. It's such a special thing that the team have achieved not to be here to demonstrate or support for them."
He added that he sees it as an opportunity to "speak up for Wales", whilst respecting the decision of others not to visit.
Whilst alcohol consumption is banned in Qatar and has been an ongoing issue surrounding this World Cup, the First Minister said fans are "not here for drink", while urging attendees to rally behind the Wales team ahead of the country's first match against the USA.
Responding to the complaints made by some supporters about the suitability of their accommodation and the backlash against the last-minute rule changes around alcohol availability in the football stadiums and other fan areas, Drakeford explained: "I think you should make the most of what is here, the fans are here for football, not for drink.
"I am sure that there will be people here who will be very keen to make sure they have the best possible time."
It comes as organisers recently announced football fans must not be "visibly under the influence of alcohol" or be shirtless at World Cup stadiums in Qatar.
An estimated £2 million has been spent on promoting Wales in Qatar, an investment that Drakeford has insisted could reap far greater returns for the nation.
He went on to meet the Wales players at a training session on Sunday afternoon at Al Saad Sports Club.
More than 2,500 Wales fans are expected to descend on Doha for Monday's opening matches.