In the end, a toothless display from the Potteries outfit meant United were able to cruise home 2-0 winners thanks to penalties either side of the interval from Javier Hernandez and Dimitar Berbatov.
However, it looks as though United will be forced to rely on 21-year-old third-choice keeper Amos at Chelsea on Sunday, which is hardly an ideal scenario.
"Anders got injured in training and David got injured at the end of training, so we had a right nightmare," said Ferguson. "Ben didn't have a lot to do but he was confident and composed, so we are pleased with that."
Stoke boss Tony Pulis admitted he wanted to work Amos more on his Premier League debut.
However, the Macclesfield-born keeper only had one shot of note to save, from substitute Cameron Jerome, as United profited from fouls by Jermaine Pennant and Jon Walters on Park Ji-sung and Antonio Valencia either side of the interval.
"The first one was very debatable," said Pulis. "The second one was [a penalty]... and the one he didn't give - for a foul on Patrice Evra - was a definite penalty."
TV replays suggested referee Mike Jones got it right with the first decision. There was little debate over the quality of Hernandez's finish and Berbatov was equally emphatic when he assumed responsibility for the second spot-kick.
"It was a very good penalty," said Ferguson of Hernandez's effort. "But he takes them for Mexico so it wasn't a problem.
"Dimitar thought he was going to take the first one so he took the second one and he scored too so we're pleased with that. It has been a good night."
The result, coupled with Manchester City's surprise defeat at Everton, means United are now level on points with their local rivals, whom they trail on goal difference.
And Pulis thinks it is shaping up to be quite a battle at the top of the standings.
"It is very open," he said. "Tottenham are still in it. Harry [Redknapp, Spurs manager] will be writing it off but he won't personally I am sure.
"He will be hanging onto their coat-tails hoping they drop points, as Manchester City have done.
"Alex will be the same and the one thing United have got over them is that they have done it before and they usually get stronger after Christmas. He will be chuffed at the results tonight [Tuesday night]."
Ferguson has his fingers crossed that Wayne Rooney, Nani and Phil Jones will all be available for Sunday's trip to Stamford Bridge, by which time Ravel Morrison might have made his debut for West Ham after leaving United earlier on Tuesday.
Morrison has been unable to shake off the off-field problems that have dogged him for far too long, and Ferguson hopes a change of scenery will trigger a change of attitude.
"In the case of Ravel it's been quite well documented," he said.
"I think he's better out of Manchester. He's got a great talent but it's how to deal with it that is important."