Henrikh Mkhitaryan netted within a minute, Romelu Lukaku scored against his former club in the 89th and Anthony Martial slotted in a penalty in the second minute of stoppage time after Morgan Schneiderlin handled.
"They wanted me, but a few things happened and I thought Everton would be the best place for me to come".
"But I'm a a little bit different - I saw at least a team, and that was a big difference between today and last Thursday - a team who had desire, togetherness and more aggression on the pitch...even with this high defeat".
He wrote in his personal blog on the back of a 4-0 victory over Everton: "We are happy, for sure, but we keep the euphoria away from the dressing room".
United will head into that game buoyed by their showing against Everton. Interestingly, three of Manchester United's goals came towards the end in the final ten minutes of the contest.
In Mourinho's programme notes before Sunday's clash, he suggested that Everton's spending suggests that they should be targeting a top four finish this season, rather than just hovering outside the top six. The new-look Manchester United look lethal in the last phase of their games.
In Sunday's other match, Chelsea was held to a 0-0 draw for the first time in nearly 20 months when Arsenal produced the type of disciplined display lacking during recent setbacks to frustrate the Premier League champions.
Lukaku, who missed a number of excellent opportunities to get off the mark in the first half, was scoring against his former club, while he also grabbed an assist after setting up Mkhitaryan's goal.
"Sometimes in football you get more than you deserve".
'That is maybe unusual after a 4-0 defeat but, yes, they were really clinical and we didn't deserve this high defeat'.
Many have called for Koeman to drop the Wales worldwide after a string of bad displays, however, it appears the Dutchman is not keen on the idea.