Costa is the Premier League's joint-leading scorer with 14 goals, but missed his side's 3-0 win over Leicester after a huge offer from the Chinese Super League club Tianjin Quanjian.
Chelsea boss Antonio Conte has reportedly fallen out with Costa, who has trained alone for the past four training sessions. Former Leicester City midfielder Savage believes the Spain striker is irreplaceable for Chelsea.
"If Chelsea lost Diego Costa, who would be their replacement for him?" BT Sport pundit Savage told Goal. "I think he has been so instrumental. He is scoring goals and I just love watching Diego Costa.
"If I could pay to watch most players in the Premier League, then I would pay to watch him because he works so hard. He scores goals, he’s energetic, he loves a tackle, he’s controversial.
"Everything I like watching in a player, I just think that, whereas before, he would get frustrated and leave a boot in, he is not doing that. He is just concentrating on closing people down, scoring goals, working hard and I think it shows.
"The game against West Brom was the one, McAuley had the ball in the corner, he pressured him into a mistake and then that finish was sensational."
Despite being irreplaceable for Chelsea, Savage concedes that Costa may not be the best finisher in the English top flight.
"Do I think he is the best in the league? I would go with Aguero. If they both went on the market, who would Barcelona and Real Madrid try to sign? I would say that they would both go for Aguero ahead of Costa.
"That’s just my opinion, I would say Aguero is closely followed by Sanchez and Costa - and I have paid my own money to watch Costa."
Costa's form has been so good that it has limited Conte's £33 million summer signing Michy Batshuayi to limited starts and Savage thinks that it is still a mystery about what the Belgium international is capable of at this level.
"He’s not had an opportunity because of the form of Diego Costa, has he?" Savage added. "If Costa’s form has been so impressive and you have to play in a 3-4-3 then there’s no room for him really.
"Costa’s form has given him no chance, so we don’t yet know what he can produce on a regular basis in the Premier League."