Boss Graeme Souness blamed poor finishing as Newcastle made hard work of despatching non-league Yeading.
Goals from Lee Bowyer and Shola Ameobi put Newcastle into the fourth round, but Souness admitted suffering some moments of anxiety.
The Magpies boss said: "Until we scored the second goal we were always holding our breath.
"As long as it was 1-0 they were in the game, and we must have missed half a dozen gilt-edged chances."
Souness paid tribute to the plucky non-leaguers who played a full part in the biggest mismatch on paper in FA Cup history, with 123 places separating the two sides.
The Newcastle boss said: "We played a spirited Yeading team who kept going and all credit to them.
"It wasn't a good passing pitch and it was a blustery day which probably suited the way they wanted to play.
"But our keeper only had two shots to save and we must have missed half a dozen gilt-edged chances."
Souness admitted the FA Cup could play an important role in Newcastle's stuttering season.
He said: "Any competition is a good one if you're still in it.
"We were on a hiding to nothing and expected to win. We're still in the draw for the fourth round and that's the most important thing."