Costa, an injury doubt before the match, opened the scoring for Chelsea in a match that would become a nine-goal thriller.
"He's a good finisher, he gives us not just that final touch but he also operates defensively and I can remember him making some tackles on the edge of the box so he is giving us what we expected," Mourinho said.
Mourinho enjoyed the feast of football but could not hide his eagerness to cut out the sloppy mistakes that saw Thibaut Courtois pick the ball out of his net three times.
"I think if the salt and pepper of football is goals then to have nine goals in a Premier League match is fantastic ingredients so I think (we saw) two teams that played the offensive way fantastically well," he said.
"We try to have the initiative so we are a different team. But I want to be different in that we play better football, score more goals, but I don't want to be different in the sense that we concede goals and to concede three goals and identify the mistakes we made is something I have to work at."
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