With Costa now in the rear-view mirror for both Conte and Chelsea, focus has turned to the future and that firmly lies with Morata - who has already made an impression at Stamford Bridge following his £58m move from Real Madrid.
Morata may have finished beautifully but the Stoke manager pointed out that the Spaniard had been helped by Stoke's own defenders.
Morata's first three Premier League goals came via his head, but a cool side-footed finish after just two minutes gave Chelsea the lead at Britannia Stadium.
Chelsea keeper Thibaut Courtois suffered an injury after falling heavily but played on. I know Alvaro well, he's a really good guy, a good person, and a good signing for Chelsea because Alvaro is only 24 years old. He is a really good guy.
However, Chelsea legend Frank Lampard was one of the few impressed by what he saw of Morata during those early days. Having shown a lack of inspiration throughout the team which has seen them gift wins to Everton and Newcastle on the road, they have risen to the title of valiant underdogs in taking four points at home from Arsenal and Manchester United.
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Pedro was the other Chelsea attacker to get on the scoresheet, but Morata stole the headlines, scoring after only two minutes before notching another two late in the second half to make it 17 goals in his last 19 games for club and country.
"It's great he got a hat-trick". We were in control of the game.
Antonio Conte has said he is looking forward to catching up with Kurt Zouma this afternoon but that will be off the pitch rather than on it as the loanee is unable to play against his parent club, meaning Bruno Martins Indi is the only centre back Stoke have available for the match.
I'm backing Conte to not allow his stars to do that, with the fiery Italian proving a motivating factor on the sidelines and his players not wanting to disappoint him before sharing the dressing room with him.
The Stoke boss lamented Costa's departure as "a real shame" and admits he will miss the striker's combative presence in the Premier League.
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