The Premier League side were nearly beaten by lower division team Coventry City.
But they did progress into the fourth round, winning 2-1 through a late Brennan Johnson goal.
Speaking on Sky Sports, Redknapp stated: “They were so poor, going nowhere fast until the goals.
“Up until then, you look at what Mark Robins did (scoring for Man United), we might look back at this goal as something similar and that's kept them in it.
“There was almost a look of embarrassment from Ange (Postecoglou - head coach) at full-time. They will be mightily relieved.
“They will be sat in the dressing room thinking "How on earth have we got away with that?" Coventry were the better side and he will be so relieved. They've got to make sure it is a turning point for them.”