Summer signing Diego Costa scored twice, with the first coming after just 35 seconds, while Branislav Ivanovic, Nemanja Matic and Ramires also found the net, with a Seamus Coleman own goal after Eden Hazard’s driving run completing the scoring.
But the Portuguese coach was less impressed to see his side concede three times, as Kevin Mirallas, Steven Naismith and former Blues striker Samuel Eto’o ensured the visitors could not relax until the final whistle blew.
Mourinho told Sky Sports: "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.
“I know they (Everton) are a good offensive side, but to concede three goals is too much. All of them I can clearly define the mistakes, the people involved and where we failed.
“We were killers in attack, especially on the counter-attack, so when you come to this stadium and get three points it is a reason to be happy. When you come here and score six goals, obviously my players did well.
"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."
Mourinho was particularly impressed with the efforts of summer signing Costa, who now has four goals from three games after his £32million summer move from Atletico Madrid.
He added: “He had three chances and scored two goals. The other one was a good save by Tim Howard.
“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.”
But Mourinho later told his post-match press conference he was disappointed with some of Everton's attempts to aggravate the striker, who was booked for clashing with Coleman and later appeared to goad the defender following his own goal.
"The only think I didn't like in this game - apart from some of our defensive mistakes - was the way some Everton players were trying to create problems for him," he said.
"I don't think this is English football. There is a good tradition with Everton teams because everything is good, everything is positive: the manager, the quality of their football.
"But to be chasing cards to a player who once more had good behaviour and was just here to play football is disappointing.
"At the end of the story Diego is maybe the best player in the Premier League in the first three matches and he has two yellow cards; one against Burnley where he didn't simulate it was a penalty and today when everyone was chasing him to get him in trouble. That is disappointing."
Chelsea are set to add to their striking options with the addition of Loic Remy from QPR, with the Stamford Bridge side triggering the release clause in his contract with a £10.5million bid.
And Mourinho is confident there will be no late hitch to the deal with the medical, after the France international saw his anticipated move to Liverpool fall through at the last minute.
He added: “The information we have from specialists in different areas is that he doesn’t have a problem to play football.”