The Spain international was left out by the Blues at the King Power Stadium amid intense speculation surrounding his future.
Antonio Conte maintained before and after the game that a back complaint was to blame for his top goalscorer missing the fixture, but Costa is the latest high-profile figure to be linked with a mega-money move to China.
Reports have also suggested that the 28-year-old has grown tired of life in England and is looking for a way out of Stamford Bridge, having previously admitted that he came close to securing a return to Atletico Madrid last summer.
Chelsea, though, have built their 2016-17 Premier League title bid around the performances of their burly frontman, with his 14-goal return helping the Blues to the top of the table.
That standing was cemented in their latest outing, as they swept aside the defending champions, but Hasselbaink feels Conte’s side are incapable of maintaining those standards without their leading marksman.
The former Blues striker told Goals on Sunday: “It’s a difficult one. For Chelsea it’s a very important one – he’s the one scoring goals and leading the line.
“They played yesterday without him but I don’t see them playing 10 games in a row without him and doing that.
“He’s a very important player. I think he’s the best striker in the league at this moment, with how he is playing.”
Hasselbaink appreciates that Costa’s head may have been turned by the offer reported to be waiting for him in Asia, with the Chinese Super League riches becoming “a problem”, but he has urged Chelsea to take a tough stance and retain the services of a prized asset.
He added: “It doesn’t surprise me. Everybody has different agendas.
“For me, I would be sad to see him go. I want to see the Costas, the Harry Kanes, the Agueros, all of those strikers I want to see in the Premier League because they make the league. It’s the best league in the world.
“Yes, the financial aspect in China at the moment is a problem. It’s a problem, but he’s still a Chelsea player and Chelsea need to be strong.”