With the Royals sitting just inside the Barclays Premier League relegation zone, many had marked this fixture as a potential upset, but the hosts' clinical finishing ensured they romped to victory against the npower League One visitors.
"If you look at the results a couple of big teams have gone out and we are thankful we are not one of them," the Reading manager said.
"I don't think we did particularly well in the first half. We just weren't ourselves. I got a bit agitated, which is unusual for me. But we were much more clinical and efficient after, so we deserved to go through."
Having looked like certainties for relegation towards the end of 2012, Reading now find themselves welcoming Chelsea to the Madejski Stadium on Wednesday on the back of a four-match winning streak.
The high morale in the camp bodes well for the Berkshire club's chances of avoiding the drop and also boosts their hopes of maintaining their strong history in the FA Cup, where they have reached the quarter-finals in two of the last three years.
"The confidence has always been good here, but winning games always breeds momentum," the 51-year-old said.
Had Chris Porter, Nick Blackman, Ryan Flynn and Kevin McDonald all taken their chances, United could have taken their hosts back to Bramall Lane for a replay. For that reason, Blades boss Danny Wilson was left to reflect on what might have been for his side.
"We are disappointed," he said.
"We take nothing away from the striking prowess of Reading. But the goals we conceded were poor - the first one in particular and the one just after half-time. I think the scoreline was a bit flattering but they have taken their chances. We had as many chances but just didn't convert them."