The Spaniard has endured a testing spell at Stamford Bridge following a big-money move from Real Madrid in the summer of 2017.
He was charged with the task of filling Diego Costa’s boots and has struggled in that role for the most part.
The 26-year-old was, however, back on target in his latest outing, with a match-winning brace recorded against Forest.
They were his first efforts in six appearances and have taken him to nine for the season.
Cudicini told reporters of a man who has admitted to being short on confidence during his time in west London: “I think he played an important part of the performance. He worked hard for the team, offensively and defensively.
“It was very important for him to score two goals. We were pleased with his performance, but even when he didn’t score. Hopefully he will be more free in his mind.
“I think Gianfranco [Zola] mentioned before the match that it is difficult when you don’t score goals.
“He is working hard in training and we knew that he could turn a corner and score goals.
“He has the possibility to score 20 goals, he is a great striker and I am sure he can do that.
“Sometimes everyone is different. Players can be more affected by the critics they can have.
“It is important he is training hard, the performance on top of the goals was important.”
Highly-rated teenager Callum Hudson-Odoi provided the assists for both of Morata’s goals against Forest.
He is currently the subject of interest from German giants Bayern Munich, with Goal having revealed that a £30 million ($38m) bid is on the table.
Chelsea are eager to keep him from the clutches of a European rival, with Cudicini conceding that the 18-year-old impressed again during a deserved start for Maurizio Sarri’s side.
The Italian said of Hudson-Odoi: “He did very well, a 360 performance.
“He worked very hard, he was running for two, his commitment was great.
“You want him to have performances like that to put doubts in Maurizio’s mind.”