Thomas Tuchel's side took a deserved lead through Christian Pulisic, but Karim Benzema scored Madrid's equaliser - which was their only shot on target - to salvage a 1-1 draw in the Spanish capital on Wednesday night.
The Blues will be disappointed not to take a lead into next week's reverse tie, with Werner missing a clear-cut opportunity from close range in the first half which was palmed away by Thibaut Courtois.
And Melchiot, the former Chelsea defender, says Werner can have no excuses for missing the gilt-edged chance.
"Sometimes you stand in front of a goalkeeper and he just makes a reaction and he touches it, but come on you're a top striker," he told talkSPORT.
"You need to grab that moment - it has to be yours. It does not matter how great the goalkeeper is.
"I was never a striker in that position all the time, but if you are my striker and you don't score that I get upset.
"When you play for Chelsea - you made the decision to go there - they are going to expect certain things from you."
Melchiot did concede that Werner did cause the Madrid backline no ends of problems and is confident he can start hitting a purple patch soon.
"The other things he brings [to the table] is what no one else can bring," the Dutchman added.
"If you look at the way Chelsea were playing, if you look at the one man can keep the whole backline busy - they were always worried about him in the moment they were pressing Real.
"You could just see the reaction… look how many times [N'Golo] Kante became free in the middle of the park because they were so worried about Werner that they couldn't press all the way through the defenders.
"So sometimes Kante slipped through it, but then it just comes for him [Werner] like that.
"I know it's sad for him because I want him to score all the time and I want him to do well.
"I don't think it will take him that long to get it right, but just at the moment when he doesn't do it we just have to call it - that's just how football works."
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Thiago Silva's wife, Isabelle da Silva, was less sympathetic towards Werner during Chelsea's draw against the LaLiga giants.
In a video uploaded to her Instagram account during the first half, Isabelle da Silva said: "This is karma, guys.
"Every team I go to there is a striker who keeps missing goals… this Werner, what is his name?"
In a second video posted on her account, she added: "We need a goal, we need to win this match but my attackers don't want to score, I don't know why they don't score."