Morata moved from Real Madrid for £58m in the summer and though he started well - netting seven times in his first seven appearances - the 25-year-old has only scored five more goals, the last of which came on Boxing Day.
His struggles are reminiscent of those Shevchenko encountered upon his switch to the capital in 2006 when he joined in a then club-record fee, with the Ukrainian netting just nine Premier League goals in 48 appearances.
Shevchenko had left AC Milan second on the club's all-time leading scorers' list and the boss of the Ukraine national team has urged Morata to be more ruthless in front of goal.
"I've seen a lot of him," revealed Shevchenko, who was speaking in his role as a Laureus ambassador.
"He's had a lot of chances. I think you need to improve the finishing when you have chances.
"It's good when a striker has chances, it's very positive. You need this for scoring goals and helping the team to win."
Chelsea face a critical few weeks having dropped out of the Premier League's top four last Sunday, with this weekend's trip to Manchester City followed by the second leg of their last-16 Champions League tie with Barcelona and an FA Cup quarter-final clash at Leicester.
Blues boss Antonio Conte has appeared increasingly unhappy with the dynamics behind the scenes at Stamford Bridge, though Shevchenko believes the mood would soon improve if the Italian could secure a few big results.
"I think he's a great manager, he's doing a fantastic job," he added.
"It's a difficult moment for Chelsea but they still have a chance to qualify for the next step of the Champions League, the Barcelona game is still open.
"It's better if you ask him if he's happy. Of course, it all depends on the results. I still think he's doing a great job. It's been a very difficult season for Chelsea - the Champions League comes, last year it was only the Premier League and he won it.
"It was a great performance, the team were playing very well, then a couple of important players left, they had a couple of injuries.
"It's a different challenge in the moment for him. A team needs to have a result. You need to get some results and everything changes quickly."
Shevchenko knows all about management having taken over his national team after Euro 2016.
And the 41-year-old has been impressed by the form of midfielder Oleksandr Zinchenko, one of his Ukraine players, filling in at full-back for Pep Guardiola's Manchester City.
"He's improving a lot," Shevchenko said of the 21-year-old Zinchenko. "It's great to see him play. Guardiola gave him the chance and he did very well. Even not playing in his position, he showed good qualities.
"Now when the player (can play) a lot of positions, it's always good for the manager. He can play differently. He is improving a lot.
"He's getting experience playing in the Premier League against great teams and great players. This is a positive moment for him.
"He is playing for one of the best coaches in the world and playing with great players, and you learn when you train and play every day with the great players."
The Laureus World Sports Awards highlight sporting excellence and recognise those who use sport to change lives for the better. For more information, head to http://www.laureus.com/awards
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