United had opened up a 4-1 lead over the Cobblers early in the second-half, but had to settle for a single point from the game as the visitors struck three times.
And although Adkins was pleased to score four goals in the game, he was left frustrated by some of the play at the back.
"We're great going forward but, you've got to defend. When we haven't got the ball everybody is a defender and, in the second-half particularly, we were shocking defensively," he said.
"The players have got to stand up and be counted. Leaders have got to stand up and do what they're supposed to do. People have got to put their head on the ball and go out and defend."
Stuart Gray, the Northampton manager, was pleased with his side's character and even felt they could have gone on to win the game.
Adkins points to lack of leadership
"In these conditions you knew anything could happen and the players showed great character to come back," he said.
"Scunthorpe have got some good players and if you give them time and space they will hurt you. After we got to grips with their strikers we got on the front foot and started causing their defenders the problems.
"
If anything I think we could have won the game, and in a way it is a disappointment to have only claimed a point."
If anything I think we could have won the game, and in a way it is a disappointment to have only claimed a point."