A Sadio Mane strike and a brace from substitute Xherdan Shaqiri condemned the Red Devils to their fifth defeat of the campaign after just 17 games.
And United's disappointing performances of late under Jose Mourinho have not been up to the standards set by former manager Sir Alex Ferguson, according to Giggs.
“In the season, you can get beat in these games,” Giggs said to Optus Sports . “When United were winning leagues, we went to Anfield and got beat plenty of times. We got beat at Old Trafford.
“It’s just within this season. Within this season it just tops it off really.
“It tops it off that it’s a disappointing season, then when you get beat by your rivals obviously your fans won’t be happy."
And Giggs feels that the players need to be held accountable for the performances they are producing.
He added: “Jose takes a lot of stick, rightly or wrongly, but the players have got to take responsibility as well.
“He’s not the one out there miscontrolling it, he’s not the one going out to Mane like Herrera did and making a stupid challenge.
“The players in that squad at the moment are better than that.
“The standards of Manchester United over the years have been high and these players have dropped below that."
However, Giggs did include Mourinho in his criticism following a start to the season that has seen United cut 19 points adrift of Liverpool at the top of the table.
“The manager has to take a lot of stick for that. We see Lukaku and Pogba in the World Cup and they’re performing to the highest level. Go back to their clubs and they’re not.
“Nineteen points behind Liverpool. That team isn’t 19 points worse than Liverpool.”