The 'Reds' swatted aside Southampton 3-0 at Anfield on Saturday to maintain their 100% start to the season and send them top of the Premier League table.
However, Moyes believes this season has come too early for the Merseysiders, saying they still have some way to go to even be considered as good as Rafa Benitez's star-studded Liverpool side of the lete-2000s..
"No, I don't think so," he told 'Goals on Sunday' after being asked if Liverpool could win the title.
"I think they've got a really good team, but you look back at teams over the years at Liverpool and they had great teams, when it was Alonso, Mascherano, Gerrard and Torres up front.
"This is a good Liverpool team as well - I don't know if it's quite as good as that team at that time. They're playing a good style, with forward players who are exceptional, and because of that I think they're a real threat."
Meanwhile, Moyes also defended Jurgen Klopp's decision to substitute Xherdan Shaqiri at half-time of Saturday's win, with the Swiss having been one of his side's better performers.
"When you play as well as he did and create goals, you're hoping to boost their confidence," he explained.
"But I think Liverpool have got a big programme coming up, I'm sure Shaqiri will play a big part in it, and maybe the manager was thinking a bit further afield than this game."