The striker arrived at the club for a fee of £32million from Villarreal and has showed promising early signs during the Blues' pre-season campaign and their start to life in the Premier League.
Jackson is yet to find the back of the net for Mauricio Pochettino's side this term, but has showed the tenacity and intent to be in the right place at the right time to make that breakthrough before long.
The chance may have arose against West Ham when Raheem Sterling was down in the penalty area, leading Enzo Fernandez to step up and take the spot-kick which he missed.
Hasselbaink was a player who had a reputation for his no-nonsense penalty-taking style during his time at Stamford Bridge and suggested that Jackson should have backed himself to take the kick in order to open his goalscoring account.
Speaking to talkSPORT, Hasselbaink said: "Nkunku being out [means] there's a lot of creativity missing for the strikers. Also now Chukwuemeka being out [means] there's a lot of creativity [missing and] hopefully his injury is not that bad.
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"I would have loved to have seen Jackson take the penalty [against West Ham] to be honest because if he scores, that would give him a little bit of confidence and he would be off the mark."
Hasselbaink added: "I've liked what I've seen. He led the line really well against Liverpool, he was a handful against West Ham.
"He just needs a little bit of help, but that also just takes time to get to know your teammates and for your teammates to know you.
"The Premier League is not an easy league. It's the hardest league [and] it's the best league. He'll be fine."