Bartlett was sent off early in their semi-final against West Ham, and the Hammers made their advantage count to win 3-1.
Midfielder Dan Barlaser was forced to don the gloves, but despite a battling performance, Newcastle came up short.
It was a disappointing end to a tournament which had seen the Magpies storm into the semi-finals with an unbeaten record, scoring six goals and conceding none from their four previous four group and knock-out games.
Coach Peter Beardsley paid tribute to his players’ efforts
He said: “We were playing well and the lads did brilliantly to get back to 1-1 with a man short and on a pitch like this, but West Ham kept the ball well and created plenty of chances with their advantage.
“It’s a real shame because we wanted to get to the final, but it’s one of those things and we will learn from it if we get invited back next year.”
Meanwhile, Newcastle youngsters Haris Vuckic and Shane Ferguson couldn’t help get Rangers promoted yesterday.
The on-loan duo both started for the Gers in their play-off final second leg against Motherwell, but were on the wrong end of a 3-0 defeat as the home side preserved their Premiership status with a 6-1 aggregate win.
Vuckic picked up a yellow card, while Ferguson was substituted after 55 largely anonymous minutes.