The Championship outfit needed extra time to get past a determined Vale side at Glanford Park on Tuesday night, but two goals in the first five minutes of the extra period sealed a deserved victory, with Paul Hayes and Grant McCann finding the net.
Scunthorpe should have put the game to bed in the regulation time but were denied by the post twice, while Port Vale's goalkeeper Chris Martin was in fine form throughout.
And Adkins was delighted with his side's performance.
"It was an excellent performance and an excellent result," he said.
"It was a historic day, I thought we played some great football and entertained the supporters. It's history because we are through to the fourth round of the Carling Cup for the first time in the club's history.
"We even gave the supporters half an hour of extra entertainment. We had 41 attempts at goal and I thought we gave them something to enjoy."
The highly-anticipated draw for the fourth round is made on Saturday lunchtime, when Scunthorpe will be in Championship action against Doncaster, and Adkins admits that the draw will be in the back of everyone's mind at Glanford Park.
"At one minute past 12 on Saturday when the fourth-round draw is made, we will be one nil up and there will be a big cheer around the ground when we get Liverpool away. That would be nice wouldn't it," he quipped.
Port Vale boss Micky Adams believes his side can be proud of their efforts as they eventually bowed out of the competition to Championship opposition after victories over both Sheffield clubs in the previous two rounds.
"I think we can be proud of what we have done tonight, with a bit of luck, it might have gone our way," he said.
"We had chances in the first half and we had chances in extra time after they scored. Their keeper played really well in extra time. It just wasn't our night."
Adams is now urging his side to take the momentum from the impressive cup run and translate that into results in League Two, where they currently sit in mid-table.
"It's all important now, we've got to take a great deal of confidence from this run and push on in the league now."