The pundit was unimpressed with two of the Blues' defenders.
The Blues almost came back into things after Loic Remy grabbed a second-half goal for the west London side.
But poor defending before and after half-time saw Jamie Vardy and Riyad Mahrez put Chelsea 2-0 up. And Savage feels Azpilicueta and Terry, in particular, were to blame after the Stamford Bridge outfit lost their ninth Premier League game of the season.
Savage told the Mirror: "I don't want to get on John Terry's case every week but I was surprised to see him working as a TV pundit 48 hours before an important game at the King Power.
"Terry was poor at Leicester on Monday night and Chelsea looked much more threatening after he came off and they switched to a 3-4-3 formation.
"For both of Leicester's goals, Cesar Azpilicueta must have known the best way to stop Riyad Mahrez is to 'show' him down towards the touchline on his less-favoured right foot. I can't believe he was twice afforded the space to cross or shoot with his left."
Terry and Azpilicueta weren't the only ones, of course, with Jamie Carragher criticising Kurt Zouma after the game for his role in Vardy's opener.
When will Chelsea's players wake up? Savage is adamant Jose Mourinho isn't to blame and feels Chelsea's senior figures are most at fault.
Next up for the Blues is a home clash against Sunderland and, even though Mourinho has been beaten by the Black Cats at Stamford Bridge before, there will be no excuses for not winning this weekend.
Can Chelsea turn things around or are things heading for absolute disaster in west London?