Slot won the Premier League at first attempt as Liverpool manager, leaving Dalglish impressed.
The Scot told the club's website: “It was a good job to get. I know Jürgen (Klopp) left and Jürgen in his own way was hugely successful at Liverpool and a great manager.
“Arne is a different breed but he is still a great manager. They had a great year last year and we’re looking forward to this year. It’s not that anybody needs to be better than somebody else, you just need to be better than the people you’re playing against.
“Taking over from Jürgen, you’re better taking over from a team that’s a good team. I think I would rather have it, with a good team than having to build one yourself.
“Now he’s seen them and had a look, maybe he’s starting to get it in his mind to make a few changes to bring in some of the people he likes, which I think is fair enough. I think it’s brilliant the way he’s gone about it.
“He had a hard act to follow and follow as well as he did. Now he’s got himself in. I’m sure we’re all looking forward to (next season).
“And he’s a really good guy. They say good people don’t normally win but I don’t think that’s the case. So, fingers crossed for him this year because he deserves it.
“He couldn’t have done any better. A really, really good job he did – and I hope it continues for him.”