The Blades' first goal in the 12th minute arrived in bizarre circumstances. A swift break down the left wing resulted in Lee Martin - on loan from Manchester United - delivering a low, piercing cross into the heart of the area.
Michael Ball was clearly confused as he completely missed his attempt at a clearance, and while Luton Shelton was almost deceived too, he managed to steady himself and score from six yards.
Explaining the situation, Eriksson said: "Sometimes you see two, three or four balloons on the pitch. I don't know how many there were out there, but there were lots.
"So before Sheffield scored we asked the fourth official to please tell the referee (Alan Wiley) to stop the match for one minute so we could clear the area.
"We received confirmation from the fourth official the referee got the message, but he didn't stop the game.
"At half-time I then heard the referee had asked Joe Hart to clear his area when the ball was up the other end of the field.
"But that's a little strange because Joe Hart has a lot of other things to do other than clear the pitch.
"I don't want to use it as an excuse, but it was a very strange goal. There were two balloons playing a one-two with Michael Ball.
"If you look at it the ball changed direction, but as I say it's not an excuse because even though they scored from a goal like that we should have been better.
"But it's something to write about because I've never seen a goal like that."
Whatever the circumstances, United boss Bryan Robson believes City "paid the price" for not clearing their area.
"Normally goalkeepers do pop the balloons because they like their box clear, and fortunately for us they didn't," remarked Robson.
Despite chances that followed for City, United added a second in the 24th minute via Jon Stead as the visiting defence struggled to clear their lines from a Derek Geary cross.
Although City's rising teenage star and half-time substitute Daniel Sturridge gave his side hope in the 48th minute with a stunning volley, City failed to mount an expected comeback.
That left Eriksson angry as he added: "We went out of the Carling Cup, but we are disappointed even more with this because we should have done better.
"We know we are a good football team, but sometimes it's not enough to just pass the ball to each other and play beautiful football.
"When you come to places like this you know the pitch is not perfect, but that's not an excuse either.
"I don't blame anything - not the balloons, not the pitch, I blame ourselves because we should have done better.
"If you don't stand up and fight, and we didn't do that in the first half, then the risk is we will end up where we did today.
"And that's the beauty of the FA Cup, but it was not very beautiful for us today."