Goals from Dave Hibbert and Joss Labadie, on loan from West Brom, gave the Shrews victory, but Crewe missed a host of chances, especially near the end when they had five strikers on the field.
Simpson conceded that the win was down to their opposition's poor finishing as opposed to Shrewsbury's good defending, and he stressed that there is room for improvement.
"It was a big three points and a massive clean sheet because it's a long time since we had one.
"So it's all smiles, it's good for confidence, not just for the defenders, but throughout the team.
"Last season we relied too much on Grant Holt. Now the goals are coming from all round the team. The problem is we keep giving them away as well."