Arne Slot's side returned to the summit of the Premier League table after beating the Blues 2-1 at Anfield on Sunday.
Goals from Mohamed Salah and Curtis Jones ensured the Reds bright start to the season continued and Richards says they can go all the way this season.
The former Manchester City defender said on Sky Sports: 'Liverpool are challengers now, there's no mistake about it. The way they can see out a game, the way they can adapt the game.
Liverpool beat Chelsea at Anfield thanks to goals by Mohamed Salah and Curtis Jones
He added: 'I think he's (Slot) brought a little bit of calmness, Defensively, Liverpool look a lot more solid.
At times under Klopp, the football he played was amazing to watch but as a defender sometimes playing in that system you could be exposed a little bit. The timing in which the defenders drop back and push up is a lot more balanced.
'You've alway got players at the top of the pitch who can win you games so it's what you can do defensively and that's why i believe they're challengers this season.'
'It was a brilliant game. Chelsea more than played their part. It feels like the first big game for Slot at Anfield,' Jamie Carragher said.
'They needed the crowd to get over the line. Liverpool weren't at their best but still found a way to win.'
Liverpool took the lead through Mohamed Salah's penalty just before the half hour mark after Levi Colwill brought down Curtis Jones.
Chelsea got on level terms three minutes after the break thanks to Nicolas Jackson's clinical finish.
But Jones poked the ball past Sanchez to regain Liverpool's lead just three minutes later and earn his side all three points at Anfield.