The club came from behind to draw 1-1 with Blackburn Rovers at St James's Park tonight.
Bradley Dack put the Championship club ahead in the second half, and Ritchie levelled from the penalty spot late in the game.
Rafa Benitez – who had made it clear before the game that he didn't have much of an appetite for a cup run – now has an unwanted replay to fit into the club's Premier League schedule.
Benitez, United's manager, had made eight changes for the tie and handed starts to Freddie Woodman, Florian Lejeune, Sean Longstaff and Jamie Sterry.
Tony Mowbray, meanwhile, only made one change to his team, and Blackburn had the better start. Newcastle just couldn't keep possession, and Sean Longstaff didn't see enough of the ball.
United's first real chance came as the half-hour mark approached. Ritchie burst forward and tested David Raya with a low shot. The goalkeeper spilled it, and Joselu's follow-up effort was deflected wide by Elliot Bennett.
Unfortunately, that was Newcastle's only real opportunity of the half, which ended goalless.
Things didn't get better after the break, and Benitez had Jonjo Shelvey, Christian Atsu and Ayoze Perez warming up.
United, however, were behind by the time Shelvey came on. Charlie Mulgrew rolled a free-kick to Bennett on the right, and his delivery was headed past Freddie Woodman by Dack.
Newcastle started playing with a bit more urgency after going behind, and Shelvey forced a save from Raya with a header from a corner. Lejeune had a follow-up effort blocked.
Benitez also sent on Christian Atsu and Ayoze Perez.
United looked to be heading out of the cup until Corry Evans tripped Perez in the box. Ritchie stepped up and converted the resulting penalty to book a replay at Ewood Park.
NEWCASTLE UNITED: Woodman, Sterry, Lejeune, Schar, Manquillo; Murphy (Atsu, 74), Longstaff (Perez, 80), Hayden (Shelvey, 57), Ritchie; Kenedy; Joselu. Subs not used: Harker, Yedlin, Clark, Rondon.
BLACKBURN ROVERS: Raya, Bell, Mulgrew, Lenihan, Travis, Dack (Williams, 85), Evans, Conway, Bennett, Armstrong (Reed, 70), Graham (Brereton, 79). Subs not used: Leutwiler, Nyambe, Rothwell, Downing.
Goals: Dack 57, Ritchie 84 (pen)
Referee: Kevin Friend (Leicestershire)