The Englishman got the nod for the central striker role against Tottenham in the Premier League on Sunday.
However, he and the rest of the team drew a blank, drawing the game 0-0 at Stamford Bridge.
Hasselbaink says Abraham must do more if he wants to keep his place in the team.
"For me Abraham has to do better," Hasselbaink told Sky Sports.
"[Reece] James cannot do any more for him, he put the ball in the right space.
"Put your head against it. The other one as well, it does not matter who you are, as a striker these are brilliant crosses.
"What do you want as a striker? These moments, this is what you want. These are the moments that are counting for Abraham and he has to step up."