Parker was speaking in the wake of the death of African-American George Floyd in the US and the protests that have followed.
Floyd was horrifically killed in police custody on May 25, prompting global outrage including from many in the world of football.
The uncomfortable truth: Sport’s response to racism still isn’t enough
It has shifted the spotlight back onto racism with the latest Game of Opinions podcast asking whether football is doing enough to stamp it out.
'How is breaking social distancing worse than racism?'
"It’s fashionable for people to be offended. I don’t want that. I don’t want people saying they’re offended if they don’t mean it," said Parker.
I really don’t get it. All I want is for people, if you’re going to say something, make sure it’s from the heart and not because you feel you have to do it.
Parker knows that football has a long way to go to having faced discrimination as a player, but said things were improving in the UK.
"For me growing up, the more mature players always said to me, 'Paul, whatever you do, you always have to be better than the white man… If you’re equal, you know which way they’re going to go'," he said.
The sad advice Paul Parker received as a youngster
"I don’t think that statement has really changed over the years, even up to now. And we’re talking 40 years minimum of me being told things like that.
"But here in the UK, you can speak out now. People will put themselves in the line of fire to go and help you. When I was playing in football, they couldn’t do because it would have affected their jobs."
'The desire to change must come from the top'
Content creator Ola Fisayo agreed that the sport must do more to create real change.
"It’s one thing to make statements and that’s one step forward," said Fisayo. "But we really are looking for systemic change, we’re looking for more people in boardrooms, in places of power, to affect the culture of our society and football too."
Yaya Toure: 'A big, big statement if players left pitch due to racism'
Football’s response has been heavily criticised in recent years with fines and empty stadiums preferred to points deductions – something that perplexes Eurosport’s Pete Sharland.
He cites the disparity between Austrian side Linz being docked six points for breaking social distancing rules while teams are ordered to play behind closed doors for repeated racism offences.
"Until football starts putting in punishment for racism, you’re not going to see any changes at all. Otherwise you’re not telling people what they’re doing is wrong," said Sharland.
"No one cares about playing with less fans. We’re in a world where we’ll have no fans for many months. So unless you can show these people that what they are doing is wrong, they’re not going to care.
"Sport can do so many amazing things but in this particular area it falls down so hard."
Schick goal gives Leverkusen 1-0 win at hapless Gladbach
'It's obvious and clear! - Arteta on penalty decision against Burnley