The victory saw Scunthorpe extend their lead at the top of League One to an impressive seven points, having registered five consecutive wins.
"The dream goes on for us and we are all enjoying it" said Adkins.
"It was not our best performance, but I have got a group of players who work so hard for each other and they deserve the success they are getting.
"The sending off was the turning point, but we went on to finish comfortable winners in the end.
"The free-kick from Dave Mulligan was one which former England skipper David Beckham would have been proud of."
Gillingham boss Ronnie Jepson was disappointed, pointing to the red card shown to Ben Chorley for holding back Jermaine Beckford as a key moment.
"I was really pleased with the way we performed and we certainly deserved something from the game," he said.
"The sending off of Chorley did change the game. It was a poor decision of his to get caught in that situation.
"We were unlucky to hit the woodwork and I also thought we should have had a penalty."