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 scalp in what was only Adams' second competitive game at the helm.
"There will be a few tears in my family after this result, 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," admitted Adams.
"We are not the most eye-catching side, but I don't think that could be labelled at us in this game. I thought we tried to play as best we could when we could and defended well, we had a bit if luck with 'Benno' but we will take it."
Hailing Vale goalkeeper Chris Martin following his sterling display, Adams continued: "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. He has done fantastically well, he has showed what a great prospect he is going to be."