The Saints endured another frustrating transfer window this summer, which saw key players depart including Danny Ings, Jannik Vestergaard and Ryan Bertrand.
However, Hassenhuttl has replaced those senior figures with younger talents including Adam Armstrong, Romain Perraud and Tino Livramento, recruitment which Moyes admires.
"I have always thought Southampton have had a good team, they have got a really good model in the way they work at the club. I think that they know their level and they know how to go about it and I think they will try to continue that again," the Hammers boss said to the press ahead of this weekend's game against the Saints.
"When you are at clubs, and I have been there before, where you have to sell players and bring other players in, sometimes you always feel the players you are selling are a big miss, but quite often it is the new young players and the players who you bring in give everybody a lift.
"It will be a tough game, every game in the Premier League is really tough. Southampton will know they will get a tough game against West Ham as well."
West Ham were also busy in this summer's transfer window, recruiting Kurt Zouma, Nikola Vlasic and Alex Kral in the final few days of last month, and all three players are in line to make their debuts for the club on Saturday.