Gavin Tomlin struck late on after Southend had soaked up pressure to end a run of three straight league defeats and halt the host's bid to close in on the top seven.
"That was a hard-working performance from us," Sturrock said. "It wasn't pretty but sometimes you have to go away from home and soak things up.
"We came to Chesterfield, who by all accounts had run over the top of Northampton here a couple of weeks ago, so when you think of that then the boys have done well for us.
"We didn't play well but football is a strange game. We've played much better than this and lost this season so we will take this against a good side.
"If you look at the stats they will wonder why they have not got something out of this game.
"But it was a very strong, hard-working and disciplined performance from us and we will take the result. Hopefully this will give us some confidence and put us back on the rails."
Marc Richards struck the crossbar with a thunderous free-kick just before half-time but the hosts were stunned with a sucker punch with seven minutes remaining when 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.