"Defensively we weren't good enough," Hessenthaler told BBC Radio Kent.
"Things have got to happen and changes made, or we can forget about going up this year. We've got to learn quickly or it's going to be a tough season."
Gillingham had only conceded one goal in four matches before the visit to Accrington and their manager was at a loss to explain it.
"As a manager and a coach it's hard to take, we've defended well for the last four games and now this. We'll watch the DVD, look at people's performances and sort it out because it's just not acceptable," he said.
Hessenthaler's side were pre-season favourites for promotion but the Accrington defeat left them 18th in the League Two table after 10 games.
"The referee had a poor game, neither of Accrington's penalties should have been given, but we just weren't good enough," said the Gillingham manager.
Accrington 7-4 Gillingham
Source: BBC Sport
Source: BBC Sport