Premier League champions Chelsea agreed to sell Spain international Costa back to Atletico Madrid on Thursday -- ending a standoff between the 28-year-old and the club for whom he was top scorer in his three seasons at Stamford Bridge.
Morata signed from Real Madrid in July for a reported fee of 58 million pounds ($78.45 million) and has quickly picked up the pace of English football, even if his style is less combative than Costa's.
The 24-year-old has scored three league goals already and Shevchenko, who never replicated his superb goalscoring record for AC Milan in three subsequent years at Chelsea, believes there is much more to come from the Spaniard.
"They have found a very good player in Morata," Shevchenko told reporters at the Best FIFA Football Award ceremony in London on Friday when Cristiano Ronaldo, Lionel Messi and Neymar were the three players shortlisted.
"He has adapted very well. They are two very different players. Costa wasn't happy so you couldn't keep him. You have to replace him and I think the club were very patient in the market and found the right player that they were looking for."
While Costa is a bulldozing centre forward never slow to go to war with central defenders, Morata goes about his business in a more refined manner, relying on stealthy movement and an ability to find space in the opposition penalty area.
A quiet game against Arsenal in the 0-0 draw last weekend led to suggestions that Morata lacked the physical presence required for the weekly Premier League combat.
Shevchenko disagrees with that assessment.
"I've been surprised that Morata has found the right chemistry with his team mates so quickly," he said.
"Of course he knows Pedro very well and (Eden) Hazard's type of game suits him very well. Morata is very good in the box and scores a lot of goals with his head.
"Chelsea create so many chances around the box, always crosses coming in from left and right and he has been clinical so far and this is a good sign for him to be successful."
Shevchenko, who is now focussed on trying to lead Ukraine to the World Cup finals as coach, acknowledged that Costa would be missed, but said a move back to Madrid was right for him.
"I think if the motivation of the player is to leave the club, it would have been unfair for the club to keep him," the 40-year-old who scored more than 100 goals for Milan, said.
"He did a great job for the club. He won two titles and was happy to be here. But he felt it was the right decision to leave the club so they were right to let him go."
Morata will be in action at Stoke City on Saturday.
($1 = 0.7393 pounds)
(Reporting by Martyn Herman; Editing by Toby Davis)
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