The 31-year-old spearheaded Everton's hopes of a point before tiring and being taken off late on - a change followed by a dramatic collapse as Henrikh Mkhitaryan, Romelu Lukaku and Anthony Martial secured a 4-0 win for the hosts.
Manchester United are now joint top of the table along with local rivals Manchester City.
"The Premier League now is becoming very trendy with five at the back", Mourinho told Sky Sports.
The model of playing an attacking midfielder alongside Wayne Rooney has already been disproven because the former United and England captain is known to drop deep and receive the ball.
This was Everton's heaviest league defeat at Old Trafford since losing 5-1 in December 1999 under Walter Smith.
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In the summer Koeman spent heavily on defensive recruits but his side have now failed to keep a clean sheet in six games, leaking in a whopping 10 goals in their last three fixtures alone. The most prolific crosser in the side is Rooney, the main striker, and Sigurdsson, who was stunning for Swansea last season, seems to have taken a step down despite moving to a much bigger club.
Everton manager Ronald Koeman: "We deserved more than we got". But he did go close 21 minutes in, meeting Cuco Martina's cut-back and sending it agonisingly wide of the bottom-left corner.
The Belgium worldwide has scored five goals in his five league appearances for his new club but did miss a great chance in the first half.
And it was let off the hook again after an hour, as Sigurdsson fought his way into the area and saw De Gea make another vital block.
And United then exploded into life to finish Everton off.
Rooney, United's record goalscorer, was the centre of attention on Sunday as he faced his old team for the first time since his summer move back to his boyhood club.