James Garner's smart finish put the Toffees ahead at the Hill Dickinson Stadium before Hayden Hackney's volley late in the first half left United with a mountain to climb after the break.

And it proved to be insurmountable as Thierno Barry's strike with 22 minutes left on the clock ended a profligate Newcastle's interest in the competition, despite Dan Burn's late consolation on a night to forget for the Magpies.

United head coach Matthias Jaissle made one change to his side for the trip to Merseyside, with Jacob Ramsey coming in for Joelinton in midfield.

Kiernan Dewsbury-Hall saw his effort deflected wide in the first attack of the game for the hosts, while Lewis Hall sliced a shot high and wide from distance at the other end.

Looking to retain momentum after Sunday's Premier League triumph at Crystal Palace, United started confidently, with Jordan Pickford having to parry Harvey Barnes' header after Nico González picked him out with a raking crossfield ball. Jacob Murphy then saw his effort blocked before Pickford spilled Joe Willock's attempt from a tight angle.

In comparison to the Toffees' England stopper, Lukáš Horníček enjoyed a quiet start to the game, but was called into action by Hackney's tame half-volley that the Czech international gathered with ease. He might have had to react swiftly to repel Tyrique George's thumping effort from the edge of the box, had Dan Burn not thrown himself in the way of it.

United frontman Will Osula was denied by a last-ditch James Tarkowski challenge just before the half hour as openings came and went but five minutes later, Everton moved in front. Pickford's long ball was chased by George, who robbed Amar Dedić on the right. Garner picked up possession and he whipped a fine first-time effort past Horníček and into the bottom right-hand corner.

Just before the break, Barnes lashed wide before tumbling under the challenge of Dewsbury-Hall in the box, but referee Farai Hallam was unmoved by the visitors' appeals for a penalty. Just moments later, they fell behind after Hallam played an advantage after Ramsey's foul on Dewsbury-Hall, allowing Barry to pick out Hackney in the box. The former Middlesbrough midfielder's finish, low and arrowed into the corner, was unerring.

Jaissle made three changes at the break, introducing Yoane Wissa, Anthony Elanga and Joelinton, with the latter making a club-record 24th appearance in the competition.

And after a terrific clipped through ball from Willock, Wissa had a sight of goal, but couldn't quite lift his header over the advancing Pickford. Dedić then took aim from range after Murphy's cross was cleared to him, but a deflection from Hackney sent it looping over the bar.

Gaps were beginning to appear in the Everton backline; Burn nodded an inswinging corner over and Dedić saw another shot blocked as the Magpies started to turn the screw before the hour as they sought a way back into the game.

Bazoumana Touré was sent on with a quarter of the contest remaining, but there was barely any time for the winger to make his presence felt before Barry made it three. Garner's pass released Dewsbury-Hall, whose cutback found the Frenchman in space and with time to fire home.

Newcastle kept grafting, and Pickford had to react quickly to keep out Willock soon after the third goal, but this was a setback for the visitors, who pulled a goal back in the closing moments when Burn headed in Elanga's cross.

Newcastle United: Lukáš Horníček, Lewis Hall, Fabian Schär, Nico González (Sean Steur 82), Will Osula (Yoane Wissa 46), Harvey Barnes (Anthony Elanga 46), Jacob Murphy (Bazoumana Touré 67), Joe Willock, Dan Burn (c), Amar Dedić, Jacob Ramsey (Joelinton 46)

Substitutes: Nick Pope, Sven Botman, Aladji Bamba, Malick Thiaw