Patrick Kluivert's fifth-minute goal proved enough for the home side who were left hanging on in the second half - Shay Given made a superb double save, Robbie Keane had a goal disallowed and we had two penalty appeals for handball against Lee Boywer waved away by referee Rob Styles.
"It was a fantastic cup-tie," said Souness. "We bossed it for 20 minutes and then I think they had most of the ball after that.
"We had Jermaine Jenas at left-back and for certainly all of the second half, we found ourselves on the back foot, other than the times when we could have sewn it up, three or four occasions when we broke and got into great positions and our final ball was not accurate enough.
"Two months ago, we would not have won that game, but there was a dogged determination about us today individually and collectively not to be beaten, not to concede anything.
"Shay Given was outstanding on three or four occasions and we have to thank him for being in the next round of the FA Cup."
Even Newcastle boss Graeme Souness admitted we were entitled to feel hard done by after his side scraped through Sunday's FA Cup quarter-final.