The Portuguese also admitted that he finds it "funny" to see his opposite number spend £75m on a defender and £67m on a goalkeeper, having criticised United's vast outlay to bring in Paul Pogba two years ago.
"It's a free world and I have no problem with Jose", said the German.
"That's okay, but maybe this season finally you demand that they win. You have to be fair and now you have to demand and say the team with investments, who are making investments that they started making last season, not just this season, last season".
Liverpool manager Jurgen Klopp has defended the decision to make Alisson the world's most expensive goalkeeper and revealed he could have opted to sign Atletico Madrid's Jan Oblak for an even bigger fee. Liverpool then reviewed the footage and Karius was advised to visit specialists Dr Ross Zafonte and Dr Lenore Herget at Boston's Massachusetts General Hospital, where he was then diagnosed with concussion. I would never talk about Manchester United if no-one asked me about it.
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But asked about this ahead of Liverpool's clash with Man United in MI on Saturday, the Reds' manager dismissed Mourinho's claims and focused on delivering attractive football for supporters.
At the time, Klopp said he would be uneasy at spending such an amount, prompting Mourinho to say: "I think if you have the money, if you invest well, is better than to have it in the bank, because the interest is very low".
Asked whether he had to win the Premier League this season, Klopp added: "I don't think so. You have to win". Do I get the sack if not? Let us know in the comments section below.
'Improvement means playing better football, being more consistent and entertaining the crowd in a very specific way - We are Liverpool and we stand for football.
"We have to deliver, we know that; what that means exactly I don't know in the moment, we will see".