But Cobblers midfielder Bradley Johnson grabbed a stoppage time winner to give his side a deserved three points.
"We were under no illusions as to how hard this game was going to be and from early on I could sense it wasn't going to be our day," said Adkins.
"All credit to Northampton, they looked a strong outfit. It was a battle, first and foremost, and Northampton did just that.
"We needed to stay in the game until half-time as I thought we could come out and win it in the second-half.
"We've got back in the game but then conceded another goal from another set piece later on.
"I would have liked to have got promotion there, but now we've got the chance to do it against Huddersfield next week in front of a full house."
Northampton manager Stuart Gray hailed the determination of his side.
"At this stage of the season, and on difficult pitches, you don't often see a classic game, but that was one," he said.
"I take a lot of pride in that performance. We came out of the traps quickly and I was disappointed not to be 2-0 up at half time.
"But there was always a chance Scunthorpe would get back in it with a player like Sharp.
"I want teams to know they've been in a game when they come here, and Scunthorpe know they've been in one."