Diaz was sold to Bayern Munich on Wednesday in a €75m deal.
Slot said from Hong Kong last night: "Yeah, it was (always going to be a sad day when Diaz left LFC).
"First of all for the person he was because he always had a smile on his face no matter what, in the year that I've worked with him. I played him a lot so then maybe it's a little bit more normal to have a smile on your face!
"But even when I didn't play him he always came out for every training session and gave it everything, with a smile on his face.
"Apart from that, I'm going to miss his song a lot, a lot, a lot as well because it was maybe one of the best songs our fans have for a player.
"And of course all that he contributed to us winning the league.
"But this is also who we are as a club. We are making big signings, we have done that over the past few years. But this club also needs to recoup funds to get these transfers that we already did over the line.
"It has been a summer where we've spent a lot but I think if people look at all the money we've already brought in, that's also – like last year when we almost only sold players – a good thing for this club as well."