It was an unsatisfactory end to an entertaining evening, when once again we showed that we are capable of being devastating in attack and clueless in defence.
Sir Bobby chose to make eight changes from Monday night’s game and Alan Shearer, Gary Speed and Jermaine Jenas were amongst those given a rest.
The visitors took an early lead when Kevin Campbell rose unchallenged to head home in the 11th minute.
But we were in charge for most of the first period and Hugo Viana, Kieron Dyer and Carl Cort all went close, before boy-of-the-moment Wayne Rooney produce a fine save from Steve Harper just before the break.
The second period started with United on the attack again, but we were unable to find an equaliser until after Sir Bobby made a trademark triple substitution, introducing Laurent Robert, Nolberto Solano and debutant Michael Chopra.
And 13 minutes from time we were on level terms when stand-in skipper Dyer latched on to a Viana through ball and slotted the ball past Richard Wright.
A minute later we were ahead when Dyer collected a Cort lay-off and unleashed a 25-yard drive into the top corner.
That should have been enough, but with just five minutes remaining, Rooney burst down the right flank and cut the ball back for old boy Steve Watson to score.
Ten minutes into extra-time there was little sympathy for another old-boy Alessandro Pistone when he inexplicably headed past his own keeper to give us a 3-2 lead.
But with eight minutes remaining Steve Caldwell handled a goal bound effort and received a red card, before David Unsworth equalised from the resulting penalty.
Then came the dreaded shoot out and when Unsworth missed Everton’s first kick it looked like the penalties jinx may be coming to an end.
But Chopra hit his penalty way over the bar and Viana and Robert saw their efforts saved by Wright and Everton progressed into the fourth round of the Worthington Cup.
Newcastle: Harper, Griffin, Dabizas, Caldwell, Elliott, Dyer, Acuna, Viana, Bernard, LuaLua, Cort. Subs: Given, Solano, Hughes, Chopra, Robert.
Everton: Wright, Naysmith, Stubbs, Weir, Pistone, Carsley, Tie Li, Unsworth, Linderoth, Rooney, Campbell. Subs: Watson, Radzinski, Simonsen, Weifeng Li, McLeod.
Referee: M Riley (W Yorkshire).