Manchester United's defence of the League Cup came to a limp end in a 3-0 home defeat by Newcastle on Wednesday as Arsenal were well-beaten 3-1 at West Ham.
Liverpool overcame Bournemouth 2-1 to progress to the quarterfinals, while Chelsea saw off Championship side Blackburn 2-0.
In a repeat of last year's final, which Erik ten Hag's men won 2-0, both managers named much-changed sides at Old Trafford.
But it was Newcastle's strength in depth that showed as United slumped to an eighth defeat in 15 games in all competitions this season -- their worst start to any campaign since 1962/63.
"This is not good enough. We have to take responsibility, I have to take responsibility," said Ten Hag.
"I feel sorry for the fans, it is below our standards, and we have to put it right."
Tino Livramento and Lewis Hall have had to wait for their chance to shine since signing for the Magpies, but the young full backs played a huge role as Eddie Howe's side got revenge for defeat at Wembley in February.
Livramento's surging run set up Miguel Almiron to open the scoring on 28 minutes.
Chelsea loanee Hall then volleyed home a brilliant effort from the edge of the box just eight minutes later.
Joe Willock's solo run and stunning finish then drew the sting from any chance of a United fightback on the hour mark.
After eliminating both City and United, Newcastle's reward is another tough draw away to Chelsea in the last eight.
Rice defeated on West Ham return
Arsenal manager Mikel Arteta was left to rue leaving Declan Rice out on his return to the London Stadium, with the England international alongside Bukayo Saka, Martin Odegaard and William Saliba on a star-studded Gunners' bench.
Aaron Ramsdale was handed a rare start since he was dropped in favour of David Raya, but it was a night to forget for the Arsenal goalkeeper.
Ben White beat Ramsdale to Jarrod Bowen's dangerous in-swinging corner but could only head into his own net after 16 minutes.
Mohammed Kudus made it 2-0 on 50 minutes with a brilliant touch and low finish from Nayef Aguerd's long ball forward.
Rice was then introduced to a mixed response from the West Ham faithful.
But any hope of an Arsenal revival was quashed by Bowen's strike from the edge of the box that Ramsdale should have done better to keep out.
"I am responsible for that," said Arteta. "We're out of the cup and we wanted to play a very different game."
Odegaard grabbed a consolation deep into stoppage time, but it was too little, too late as Arsenal's 30-year wait to win the League Cup goes on.
Liverpool, Chelsea progress
Liverpool had to see off a spirited effort from Bournemouth and appalling weather conditions as Storm Ciaran swept in at the Vitality Stadium.
Justin Kluivert had cancelled out Cody Gakpo's opener with his first Bournemouth goal.
But Darwin Nunez came off the bench to win the tie with a spectacular dipping strike from outside the box.
Liverpool boss Jurgen Klopp said victory would make a long journey back north on the team bus rather than a flight due to the stormy weather more palatable.
"Now we drive home. Long trip. But with going to the next round, it feels much better," said Klopp.
Liverpool will host West Ham in the quarter-finals next month.
Benoit Badiashile and Raheem Sterling were on target as Chelsea secured a rare home win under Mauricio Pochettino to reach the last eight.
Everton's upturn in form continued with a comfortable 3-0 win over Burnley.
James Tarkowski, Amadou Onana and Ashley Young scored on the night the Toffees remembered former chairman Bill Kenwright, who died aged 78 last week.
Fulham will travel to Goodison Park in the next round after they avoided an upset by winning 3-1 at Championship high-flyers Ipswich.
League One Port Vale host Middlesbrough in the other quarter final.