Midfielder Brian Howard scrambled in the only goal of the game on the hour mark to lift the Blades above Birmingham on goal difference with just four games left.
Alex McLeish's side face bottom side Charlton at The Valley on Saturday and Blackwell believes they are still in the driving seat.
He said: "It's another win on the long road to the Premier League but that's all it is.
"We knew it would be tough here against an excellent Reading side and that proved to be the case.
"If my players were not such strong characters then they would not have won that game but they have been phenomenal for me all season.
"Of course psychologically it is a boost for us all to be in the top two but we have four games left.
"I would like to go second on the last day of the season if it was down to me but it's not down to me.
"Birmingham play tomorrow and we know that they can win but it is a brilliant feeling.
"We have put ourselves there to be shot at now, they have a game in hand so let's see what happens."
While Blades fans may be getting carried away with thoughts of another season in the top flight Blackwell revealed there would be no celebration for him this weekend.
He said: "I am going home now to see my dog Chester. He is my best mate and he got diagnosed with cancer last night so that brings you back down to earth.
"I'll say goodbye to him and then we will prepare for Nottingham Forest on Monday."
A tense game exploded into life in the 58th minute when Royals striker Dave Kitson thundered a header against the crossbar.
But 60 seconds later Jamie Ward's deep cross was looped back over Marcus Hahnemann by Matthew Kilgallon - only for the ball to hit the crossbar.
However, Howard was alert to the rebound and his right-footed drive squirmed off an attempted block from Stephen Hunt and dribbled into the bottom corner.
Reading look a shadow of the side that were routinely trouncing all- comers at home in the early months of the season and are limping toward a play-off place after looking set for automatic promotion much of the season.
Boss Steve Coppell admitted his side's plight was preventing him from sleeping but refused to concede automatic promotion was out of his hands.
He said: "At the start of the season you want to win promotion and with five games to go we need to win five games to give ourselves a chance of achieving that.
"If we'd have won today we would be in the same position so in a sense nothing has changed.
"But our home form is a massive worry. It is giving me sleepless nights and I have got to get home for another one of those now.
"It's something which is bemusing. To be so strong for so long and now we have lost four and drawn two of the last six here baffles me.
"I don't know what's going on or else I would have changed it."
The first half was held up for seven minutes while midfielder Kalifa Cisse was treated after a challenge from Darius Henderson but Coppell believes he will be fine.
He said: "Cisse had some whiplash from the way he fell.
"We think the x-rays are clear but you have to be safe rather than sorry in those situations.
"It looked a bit melodramatic going off on a golf cart but you can't take a risk with a neck injury. We'll see how he is."
Sporting Life