Mourinho arrived at Tottenham Hotspur Stadium last November and guided a struggling Spurs side to sixth and a Europa League place, but improvement was anticipated heading into the new campaign.
Tottenham were outplayed by Everton, though, who gave debuts to James Rodriguez, Allan and Abdoulaye Doucoure and might have led long before Calvert-Lewin's brilliant 55th-minute header.
Mourinho's men could not muster a response and are already searching for answers at the start of a brutal stretch in which they could play as many as nine matches before the October international break.
Everton were gifted a huge chance to take the lead after 16 minutes as Ben Davies' wayward crossfield ball escaped Toby Alderweireld and the alert Richarlison pounced.