The Portuguese bemoaned the lack of a cutting edge after creating numerous scoring chances and dominating possession against Everton, following a goalless draw in their last league outing at Manchester United.
It was the fourth time in five games in all competitions this season that Chelsea's central strikers had drawn a blank, with the goals they have scored coming principally from midfield.
While the west Londoners have found the net on six occasions overall, Fernando Torres's strike in the European Super Cup shootout defeat by Bayern Munich remains the only goal notched by any of their centre forwards.
New signing Samuel Eto'o, brought in from Anzhi Makhachkala at the tail-end of the transfer window, was the latest to play as the lone frontman on Saturday but fared no better than his predecessors, fluffing several chances.
The Cameroon striker headed a cross from Ramires over the bar after five minutes, had an effort in front of an open goal blocked by Gareth Barry and then scuffed a shot wide at the start of the second half in a profligate display.
Eto'o was not to blame for the defeat, Mourinho said before adding the team's display highlighted a missing characteristic.
"I don't think it is a question of sharpness but perhaps no killer instinct in this game," the manager told reporters.
"In the second half a Branislav Ivanovic cross and Eto'o at the first post, he has scored 100 of these goals in his career. Samuel was a killer (in front of goal) all his career."
Mourinho's decision to bring Eto'o in from the Russian cold and then thrust him straight into the limelight suggests he hopes he can become the trusted lieutenant he had in Didier Drogba in his first stint at the club.
The Cameroonian was part of his Champions League-winning side at Inter Milan in 2010 but is now 32 and coming towards the end of a centre forward's normal shelf life.
Chelsea made a much-publicised attempt to lure Manchester United's Wayne Rooney to the club in the close season and may be tempted to renew their efforts in January should the Eto'o experiment prove fruitless.
After starting only two of their five competitive games, it seems Mourinho is unconvinced Torres can return to the goalscoring form that persuaded Chelsea to pay Liverpool 50 million pounds ($79.33 million) for him in 2011.
Torres's Spain team mate Juan Mata is another who seems to be out of favour with the Portuguese.
Mata was hauled off after 57 minutes, having made only his second start of the season, although Mourinho was adamant the decision was a simple tactical switch.
"I took Mata off, I tried Oscar - the same position but a different player as Mata is more a passer, Oscar more individual creation and maybe he should have had a penalty," the Portuguese said.
Mourinho's counterpart at Everton, Roberto Martinez, celebrated a first win of the season after beginning his time at the club with three straight draws.
"It wasn't the perfect performance from our point of view but we showed character and all the attributes needed to be a winning side," said the Spaniard who left Wigan Athletic in the close season to replace David Moyes.
"We gave away two or three chances from not keeping the ball well enough but the way we reacted, took responsibility and defended was immense.
"Throughout the game I thought we always carried a threat. Chelsea are a team well recognised for their defensive strength but I thought we were unfortunate not to score more than one goal," said Martinez.
"It was one of those performances as a manager where you couldn't be prouder."