Cook saw his team control the game but they could not add to Jay O'Shea's 19th-minute header which was enough to clinch the points.
The hosts should have been out of sight by then with Eoin Doyle twice being denied by ex-Chesterfield goalkeeper Barry Roche early in the second half while, at the other end, Sam Morsy rattled the Morecambe bar with 11 minutes left.
But the victory keeps Chesterfield six points in front of fourth-placed Fleetwood and Cook said: "We played really well.
"We dominated possession, moved the ball and created clear-cut chances but unfortunately couldn't get that second goal which would have made it a more comfortable night.
"That was the disappointing thing, not getting that second goal and when we break it down, our Achilles heel is not putting teams away - we know that.
"It's something I try and solve every day and I'm thinking about trying to get (Fernando) Torres from Chelsea but I don't think the chairman is too keen!
"But I thought we had a lot of good performances and it was a very accomplished performance by our lads to win the game and to have a clean sheet."
Cook now turns his attention to Sunday's Johnstone's Paint Trophy final against Peterborough at Wembley and he admitted: "It's going to break my heart to leave lads off that bench because everyone has families going down.
"Sometimes as a manager you can care too much and I certainly do."
- Sports & Recreation