Brendan Rodgers blamed a lack of concentration as Leicester were stunned by Newcastle.
Joe Willock and Paul Dummett put the visitors 2-0 up at the break against the FA Cup finalists.
Callum Wilson then struck a double to take his tally to 12 goals.
Marc Albrighton and Kelechi Iheanacho halved the deficit late on to briefly give the third-placed hosts hopes of a comeback.
But the defeat is a huge dent to the Foxes’ top four bid after being held at 10-man Southampton previously.
They also take on Chelsea a week today at Wembley in the club’s first FA Cup final in 52 years.
Boss Rodgers rued: “We made so many mistakes, you can’t afford to do that for the goals we conceded.
“It is very frustrating. It is a period of the season where you need to be super concentrated.
“We are close to achieving what we want to achieve but we lacked concentration.
“But I am proud of the players because they kept going right until the very end.
“The players are bitterly disappointed but we have to stick together and go again on Tuesday.”
The Foxes lost influential defender Jonny Evans to a heel injury in the warm up.
“For him to come out was obviously a big blow for us.
“We have three tough League games to come but all against teams we have beaten over the course of the season.”
Newcastle, who have lost just once in six games, climb to 13th -12 points above the drop zone.
Magpies boss Steve Bruce said: “I didn’t think we would be coming here and scoring four times but we played very well.
“That first half was as well as we have played since I have been in charge.
“I enjoyed watching us play. Our big players being back has made a difference and is the real change. I am very pleased.
“We made it a bit hairy at the end but thankfully we came through.”
Two goal Wilson said: “We can start looking upwards.”
The victory marked a double boost for Newcastle after HMRC confirmed they have ended an investigation into the club’s tax affairs.
Sign up to the Mirror Football email here for the latest news and transfer gossip.