Alexander-Arnold intimated that City's lavish spending made their success less meaningful.
Speaking to FourFourTwo magazine, Alexander-Arnold said: "You're up against a machine that's built to win that's the simplest way to describe City and their organization.
"Looking back on this era, although they've won more titles than us and have probably been more successful, our trophies will mean more to us and our fanbase because of the situations at both clubs, financially. How both clubs have built their teams and the manner in which we've done it probably means more to our fans."
"If he wants to say that, OK," Haaland responded.
"I've been here one year and I won the treble and it was quite a nice feeling. I don't think he knows this feeling. That's what I felt last season, it was quite nice."
Speaking to BBC Radio Manchester, Dias added: "We've won a lot in this club, especially last year with the Treble. I think it's pretty certain between us, between our fans, how much it meant to all of us.
"At the end of the day you can only have certain emotions if you actually win stuff. A Treble is a feeling you can only know how it feels when you actually do it.
"I think in a club like Man City and my previous club (Benfica) our greatness will be shown in a way that these comments don't affect us. We know what we've done, we know what we've conquered, we know what we're going for in what's to come. We don't do it for anyone else, we do it for ourselves.