Lukaku goes into Sunday's heavyweight clash against former club Chelsea having failed to find the net in six games.
That barren run sits in sharp contrast to his early outings for the Red Devils, where he scored in all but one of his first 10 appearances.
United boss Jose Mourinho declared the Belgian "untouchable" from fan criticism, but then intervened to stop him taking a penalty against Benfica in midweek.
"Lukaku is a magnificent striker, but he's going to have difficult times and it's important people are backing him, cheering him on, making him feel he's wanted," Hasselbaink told Press Association Sport at a Sure Pressure Series event.
"That kind of thing is important as a striker, especially when you sign for a fee like £75million, especially when you play for a big club like Manchester United
You have to be mentally strong because you're going to have a period where things are not going for you.
"That doesn't mean you're a bad player or that all of a sudden you're not worth the money or you can't do it anymore, it's just how it is.
"But you are the only one who can get yourself out of it
The ball will go in again, but he has to be strong minded because you're always under pressure at Manchester United."
Hasselbaink, a two-time Premier League golden boot winner, does not expect a glut of goals at his old stomping ground and instead expects Jose Mourinho's pragmatic tactics to keep the scoreline tight.
"I don't there's going to be a lot in it, it's probably a 1-0 game," said the Northampton boss.
"I hope Chelsea get the win, but it won't be too open
Mourinho will want to win, but won't want to put everything on it
In the big games he plays it very tactically a lot of the time.
"It will be interesting, but I don't think we'll see a lot of goals."
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Source : PA
Source: PA