The Spireites could not break down a solid Shrimpers defence and the visitors won it when Gavin Tomlin went clear with seven minutes to play.
Chesterfield shaded the possession in a low key first half but neither goal came under threat until Marc Richards thundered a 25-yard free-kick against the underside of the crossbar in the 41st minute before forcing goalkeeper Paul Smith to push out another fierce strike 60 seconds later.
Southend continued to frustrate the Spireites after the break, although Danny Whitaker saw a dipping 20-yard shot just clear the bar before a low cross almost fell to Jack Lester.
The visitors had created little since the opening minutes but they stunned the hosts with a sucker punch in the 83rd minute.
Michael Timlin robbed Sam Togwell inside the Chesterfield half and sent Tomlin clear and he placed a right-foot shot inside Tommy Lee's left-hand post.
Cook said: "I think we did enough to certainly not get beat. But what we have to be careful of is that when we don't win, we don't lose.
"It's a bit of a problem for us at the minute that when we do okay, we end up losing.
"Every game is a big opportunity in this league, every single game you play you must respect. It's irrelevant who you play, there's no such thing as an easy game and you must prepare properly.
"It's all about what you do and your preparation and when you've finished the game, you've done everything in your power to win and certainly we didn't do that and it wasn't our day."