"They showed more desire than us and more motivation, but in this case the fault is with the coach", Conte said. "The kid played fantastically well, but everybody fought and did what they had to do".
Chelsea's trip to Goodison Park is the most hard of their six remaining fixtures - Everton are flying at home, where they have won seven league games in a row.
Matteo Darmian has tipped his Manchester United team-mate Marcus Rashford to become "one of the most important players in the world", once he fulfils his incredible potential.
United know getting their hands on the Europa League trophy will deliver a Champions League place next term and that 28-goal Ibrahimovic is feeling fresher after being ordered to take things easier in recent days.
Fabregas came on in the last 10 minutes at Old Trafford, when Chelsea were crying out for him in the first half as they were very predictable in possession.
"It is disturbing moving forward, it is a glimpse moving forward for Chelsea if they are going to drop so far with one or two injuries, they do need to strengthen that squad".
"Firstly, with the Liverpool and Manchester City victories, if we didn't win it's goodbye to the Premier League [finishing in the top four]".
"I think Marcus is a great player", the Italy full-back said.
'He is still very, very young and I think he is very important for us. "These three points were phenomenal".
"We have to think that there are six finals from now until the end. They are named Chelsea, but they could be named Arsenal, or Tottenham, or another one".
The given defeat means that Antonio Conte's side are now four points clear of London counterparts Tottenham at the top of the Premier League.
"But it's a great feeling to know that it's hard for us to lose a match, people fight until the end".
"We have a lot of match-winners".
Lampard also felt the absence of Thibaut Courtois and Marcos Alonso hit Chelsea hard.
Conte refused to comment on rumours the Belgian had suffered the injury playing basketball. Eventually you can take control of the situation, even if you do go a goal down. I think it would suit both of them, but that's for the manager to decide.