United never recovered from conceding two goals in the opening thrusts of the match, with veteran Tigers striker Dean Windass striking after five and 16 minutes.
Jonathan Forte netted on the stroke of half-time, but although Scunthorpe made a contest of it in the second period they rarely threatend visiting keeper Boaz Myhill.
But Adkins was left reflecting on a decision of referee Uriah Rennie not to give a spot-kick when Sam Ricketts appeared to trip Martin Paterson, insisting: "It was a clear penalty.
"The referee ws standing 10 yards away, the player tackled Paterson and took his ankle away. It was clear penalty but the referee didn't give it.
"In the past two games the referee has been big enough to turn around and say he'd made a mistake, but will this one? I can't see it.
"We tried to be creative and give the players some license to move around the park. We tried to throw the kitchen sink at them.
"It wasn't a fair result, but it's the result that stands. Two goals in the opening 16 minutes hurt us. All of a sudden it was an uphill challenge.
"We got back in the game but we couldn't appreciate how strong the wind was.
"We tried to get the ball down and play through them. There was some great character from the players."
Tigers boss Phil Brown was delighted to give his supporters something to shout about after experiencing his first ever Humber derby.
"The preparations for the game went well and we wanted to come out with the bragging rights, not that we'll do that," he said.
"It was a strange game, because they scored just before half-time it left me thinking.
"I thought I could quite easily kick off at the players but I thought that if someone had offered me a 2-1 half-time lead, I would have taken it.
"They threw everything at us and it was an ugly second half but we showed a lot of character in defence, but we could have easily caught them on the counter attack three or four times."