Two goals from striker Marc Richards, one greatly assisted by a howler from Blades goalkeeper Ian Bennett, either side of a Billy Sharp equaliser gave Vale the victory and Blackwell expressed concern at his side's showing.
"There were no plusses. I give people opportunities to perform and they didn't impress me," said a furious Blackwell.
"I put a team out I thought capable of winning but tonight four or five of them have let themselves down badly and I mean badly.
"We've had enough chances to win by a cricket score. But if you don't take them you are going to get punished, I don't care what level you play at. Once again missed opportunities and we have paid the price."
Blackwell was full of praise for young Vale goalkeeper Chris Martin after he produced a string of fine saves to keep United at bay.
"There were two or three world-class saves there, he can be very proud of himself tonight, I thought he was superb," he added.
Vale boss Micky Adams was equally complimentary about his stopper and is tipping him for big things.
"Before I got to the club they said he had done well at the end of last season, but you are always wary of an 18-year-old kid," said Adams.
"He has done fantastically well, he has showed what a great prospect he is going to be."
Adams, a life-long Sheffield United fan, joked his family would have been upset at the result, but is glad to have made a mark at Vale so early in his tenure.
"From a personal point of view I am the only one gutted," he quipped.
"There will be a few tears in my family tonight, but I am new to the football club and it is important that I stamp my mark on it and results like this will only help me.
"We are not the most eye-catching side, but I don't think that could be labelled at us tonight.
"I thought we tried to play as best we could when we could and defended well and had a bit if luck with 'Benno' but we will take it."