It was the kind of booking that drives managers to distraction, especially as it was Morata's fifth of the season which activated an automatic one-match ban. The closest they actually came to a goal was when Ashley Williams headed against his own crossbar.
There is plenty for Conte and his team to reflect on what was another deflating result in the Premier League.
Everton defender Phil Jagielka made two goal-line clearances in quick succession to stymie the hosts and at haul-time, it seemed only a matter of time before the Blues would find the opener.More news: Samsung Galaxy J7 Nxt with 3 GB RAM appears
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"We tried to make changes at half-time to give us a better platform to get up the pitch a little bit more and I'd have to say that didn't work as well as I would have liked because our quality of ball wasn't as good as I wanted".
But their efforts to hit the net were frustrated by Everton's keeper Jordan Pickford, who blocked them.
On the other end, Thibaut Courtois was a virtual spectator as Sam Allardyce's men did not have a single shot on goal over the course of 90 minutes, perhaps lacking penetration without in-form striker Wayne Rooney, who sat out the tie with an illness. "You can see this during the game", he said. We had a good couple of chances, we kept a clean sheet against the champions - it shows great character.
Morata will be back for Chelsea's home match against Brighton and Hove Albion on Boxing Day.