England players Marcus Rashford, Bukayo Saka and Jadon Sancho were all targeted with racial abuse on social media following the Three Lions' penalty shoot-out defeat to Italy in the Euro 2020 final on Sunday.
The FA and UK Prime Minister Boris Johnson released statements condemning the abuse, while Gareth Southgate and England captain Harry Kane reiterated the stance of England's squad, who have taken the knee prior to kick-off in every game of Euro 2020.
A mural of Rashford in Manchester was also defaced, though well-wishers covered the graffiti with messages of support for the 23-year-old, whose efforts off the pitch have resulted in a government policy shift over the last year.
But Triesman, a member of the House of Lords who was the FA's chairman from 2008 to 2010, insists now is the time for stricter action.
"Well, it is a way in which people show their beliefs and their solidarity with their colleagues who come from different ethnic backgrounds and that's not a bad thing," Triesman told Stats Perform when asked for his views on England taking the knee.
"The fact that people do something that's visible together, I don't think is a bad thing. But I think what we must get past is politicians saying that they don't like it or saying that it's outrageous, and saying it [racism] cannot be tolerated, and then doing nothing about it, which is tantamount to tolerating it.
"And that's why I think it has to be translated into action. I really, I think it's true in many things in life, it's certainly true in politics, but it's true in football as well. It's not so much what you say, it's what you do. It's when people see what you do, and they can see what you say and what you're doing are the same thing.
"The change will only come if the football authorities and political authorities come together and say they are going to make changes and spell out what those changes are.
"I think that part of this has to be a legislative change in which the people who run the media platforms so often just describe themselves as the postman, they don't know what's under the envelope. I don't buy that at all. That's a recipe for seeing children abused online. It's a recipe for bullying.
"We've seen all of these things. It's not like they're a mystery to us anymore and I think the media platforms have got to be held to account, even if it means that a very rich source of the material that goes on to them is simply cut off. There's a point at which people have to face their responsibilities."
Triesman added that the onus is also on the FA to take tougher action, as well as lobbying the government.
"If we catch them in grounds being racist and abusive, that should be the last day they get into a ground to see football," he continued.
"Stamp it out. Football can do a lot of this itself. But if it needs extra powers – if I was still at the FA I would be knocking on the door of government today saying, 'Here are the powers I've got, I'm going to use them. If I think they're deficient, I want more powers, because I'm absolutely determined'."