After receiving criticism following a big miss against Arsenal, goals will cast the deciding vote in an argument which could go either way and a goal this weekend will help both Morata and Chelsea.
Chelsea keeper Thibaut Courtois suffered an injury after falling heavily but played on.
Morata was also on target in Chelsea's last away game in a 2-1 success against Leicester.
"I know Alvaro well, he's a really good guy, a good person", Conte told reporters.
Fans couldn't watch Premier League games like Manchester United taking on Southampton and Chelsea facing Stoke City.
Chelsea scored from its only two shots in the first half, Morata putting the team in front after just 82 seconds before fellow Spain worldwide Pedro netted his second goal in his last three games.
The Spanish striker then rounded off the win with two goals in the final quarter-hour to take his Premier League tally this season to six.
By coming from behind to beat Bournemouth, Everton have dragged themselves out of the bottom three after a second league win this season.
"I can not be too disappointed given the circumstances, we had a good go at it but they had too much quality in the end to take it away from us". "I think the last two goals embellished the result".
Conte also provided an update on Eden Hazard and says the Belgian global is now fully recovered from his foot injury and is able to start matches after coming through the Forest game unscathed in midweek.
And perhaps now Costa has gone for good, and his shadow gone with him, Morata can kick on and show that his early season form is more than just a good start.
"Now he has to continue this way to be a great striker", Conte said.
At the Goodison Park, Everton fought back to prevent a fought straight defeat, as they won 2-1 over Bournemouth.
"I like him because he's a complete player and also he has a lot of room to improve in every situation, tactical, physical, technical aspect, he's very committed, his behaviour is always fantastic". But Stoke is a tough team to play and it's the first of three hard games'.
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