Steve Bruce accused his Newcastle players of "switching off" after West Brom threatened an unlikely comeback before the Magpies reached the FA Cup quarter-finals for the first time since 2006.
Inspired by two-goal Miguel Almiron, the Magpies raced into a 3-0 lead at The Hawthorns but were left hanging on as the Championship leaders rallied to score two late goals.
"Unfortunately it's in our DNA," a relieved Bruce, whose side are battling to stay away from the Premier League relegation zone, told BBC Sport.
"When we went 3-0 up we switched off. Sometimes you think it's too easy and suddenly they get a goal back.
"It wouldn't be Newcastle if we didn't do something like that. We made hard work of it."