"We totally controlled the game - it was a lesson in football. Carlisle are a very good side but we dominated throughout," said Adkins, who was confirmed as Brian Laws' replacement earlier in the week.
"It was a great goal from Sharp but he is the sort of player who will work his socks off for the team.
"This was all about the team rather than an individual. We kept a clean sheet and gave a disciplined performance and the work ethic right through the side was superb."
Sharp's goal shortly after the half-time break was remarkably his 17th of the season, but Keogh's stoppage time lob from 40 yards will get all the plaudits.
Carlisle boss Neil McDonald had no qualms about the final result
"They deserved it although I don't think they were two goals better," he said.
"They are the best team we've played all season. They have a bit of pace and Sharp only needed once chance to show why he is top scorer.
"The last couple of games have shown that maybe we need to bring in a bit of quality. Scunthorpe showed us what that is all about - they had a bit of class."