Premier League players, for example, will have their names replaced by 'Black Lives Matter' on the back of their shirts for the first 12 matches of the restarted campaign.
A Black Lives Matter logo, along with a badge thanking the NHS, will also feature on their kits for the remainder of the 2019-20 season.
Players and staff from Aston Villa, Sheffield United, Manchester City and Arsenal all knelt prior to kick-off on Wednesday in support of the movement for racial equality.
Meanwhile, Liverpool captain Jordan Henderson helped set up the #PlayersTogether cause in April that sees top-flight players raise funds for NHS Charities Together.
And Manchester United's Marcus Rashford was successful this past week in his campaign to ensure around 1.3 million children in England would be eligible for school meal vouchers during the holidays.
Asked about players using their stage to bring about social change, Klopp told a press conference: "Let's start maybe with the first one, what Hendo and the players did during the lockdown.
"I'm proud of the players but I'm not surprised because I know that the players do a lot of things without really talking about it. That's what makes me proud.
"I was not surprised that the players will be immediately ready to help in this difficult time.
"What Marcus Rashford did, I couldn't respect it more, it's unbelievable. It's a little bit of a shame that he had to do it, because things like this should be just natural, but there was something to do and he did the job in an incredible manner.
"What he did during the lockdown was absolutely fantastic."
The Reds boss continued: "Black Lives Matter, that's another thing which I hope, especially in this case, it's the last time that we have to make sure everybody hears and sees that, because it's too long that we already deal with these kind of things for reasons I really don't understand.
"If football is a role model for anything in life, then it's for that – for equality. That everybody is exactly the same – wherever you come from, wherever you are from, absolutely the same.
"It's all about who you are, not which colour you have or whatever or which haircut or whatever.
"I know from my point of view it's easy to say that but it's not easy for me... people may think it's easy for [me] to say that, but it's not easy. It's just for us in football completely natural – and that's how it should be everywhere.
"Judge people only because of who they are and not any other things.
"It's so dumb, so unbelievably dumb [for] not doing it like this. It's really hard for me to even understand it a little bit why it could be like this.
"But it is like this and so we have to stand up or we have to kneel. Whatever we have to do, we have to do and we will do, 100 per cent, just to sort this situation for now and for the future because the past we cannot change, but the future we can change and that's what we all should try."