Second-half goals from Lee Bowyer and Shola Ameobi gave Newcastle a 2-0 victory over the Ryman League side which owed more to the Premiership club's superior fitness than any vast gulf in class.
The Newcastle manager, however, explained Yeading were causing his side so many problems in a goalless first-half he feared Bramble, booked for a 28th minute foul on Darti Brown, would get sent off.
"In the first half we weren't competing enough and I took Bramble off in case he got sent off," said Souness.
"If we had gone down to 10 men it would have been very tight. Their game plan was to get in there among us and test our resolve and in the first half we were losing too many 50-50s.
"But in the second half we went up a gear. I expected us to be like that from the first minute. They pushed us all the way but we were guilty of missing some great chances. We scored two but we could have had another four or five. Until the second goal went in it was game on."
Souness admitted it was the type of physical challenge he used to relish as Liverpool's tough-guy midfielder.
"It was a proper game of football, the sort I would have loved to have played in," he said.
"That's how it should be. They got the best out of their players and as long as it was 2-0 they still had a chance, especially as the swirling wind and the bobbly pitch gave us a hard time.
"But this is what the FA Cup's always been about. It's a great competition, although it's not always been kind to me. The BBC were screening it live, all the press were here wanting us to give them some screaming headlines."
Souness also admitted he was thankful the match had not gone ahead at Yeading's tiny ground. The tie was switched to Loftus Road for safety reasons.
Meanwhile, Yeading manager Johnson Hippolyte, who publicly thanked the club's supporters on the pitch after the match, had nothing but praise for his players.
"Apart from the birth of my children it was the second proudest day of my life," he said.
"At half-time I said to my players keep doing what you are doing and Bramble will be sent off Souness obviously knows his stuff.
"We competed with them mentally but our problem was always going to be our legs and that's how it was."
Hippolyte also said he hoped the performance would alter the view of Newcastle chairman Freddy Shepherd, who recently proclaimed the big clubs had little concern for the fate of football's minnows.
"I hope it does," he said. "We all know we put on a good show today and it didn't look like the biggest mismatch in FA Cup history did it?"
Hippolyte also revealed he and Souness had had a minor disagreement on the touchline because the Newcastle manager thought he was influencing the fourth official.
But Hippolyte hoped the performance would persuade Newcastle to offer Yeading a pre-season friendly at St James' Park.
"We all want to progress and I think if we can continue playing like this the club will do so," said Hippolyte.
"Now we have got to focus on the league on Saturday. As great as this has been that is the most important thing for us."
Typifying the Yeading resolve was goalkeeper Delroy Preddie, who broke the little finger in his right hand after producing a flying save from Newcastle midfielder Jermaine Jenas but played on after treatment.
It would have impressed watching England manager Sven-Goran Eriksson, for whom Hippolyte had a message.
"I heard he's looking for a coach," joked Hippolyte, who fits kitchen worktops for a living.
"I'll have some of that."
YEADING: Preddie, Nevin Saroya, Marc Leach, Stanley, Barima (Behzadi 74), Haule, Darti Brown, Clarke, Protain (Woodruffe 78), Telemaque (Quamina 84), DJ Campbell.
NEWCASTLE: Harper, Taylor, Boumsong, Bramble (Andrew O'Brien 45), Babayaro, N'Zogbia (Ambrose 39), Jenas, Bowyer, Robert (Milner 70), Bellamy, Ameobi.
Referee: H Webb (S Yorkshire).