Ebiowei had his decisive spot-kick in the shootout saved by Nick Pope, as a much-changed Palace crashed out of the Carabao Cup.
The 19-year-old summer signing from Derby was visibly upset afterwards and Vieira said: “It is normal for him to get upset. I like to see him upset, this is a good reaction to have and an experience which will make him improve.
“It is a step he will make forward, because sometimes to progress you have to go through difficult periods.
“We feel sorry for him as a young player, but you have to go through those moments to learn. He will come back from that and we will give him the support he needs.”
England goalkeeper Pope was the hero for Newcastle, saving penalties from Luka Milivojevic, Jean-Philippe Mateta and Ebiowei in the shootout.
But there were positives for Palace and stand-in goalkeeper Sam Johnstone impressed on only his second appearance since joining the Eagles on a free transfer in the summer.
Vieira, whose side play at Nottingham Forest on Saturday in their final game before the World Cup, said: “He did some good play when we wanted to build up from the back, he made some really good decisions and he did really well.
“The positive is [that] we have a really clear identity about the way we want to play the game, regardless of the players on the field. We showed quality at times.”