Graham Alexander's men have now failed to score in three consecutive matches, while the result moved Danny Wilson's team two points clear of the relegation zone.
It took just minutes for Fleetwood to create a fine opportunity at Highbury Stadium, but Gareth Evans failed to get enough height on his attempted dink on Wednesday.
Stephen Dobbie and Jamie Proctor also threatened for Fleetwood, who breathed a sigh of relief when Dale Jennings' strike rattled the woodwork.
In the final minute of normal time, Fleetwood's Josh Morris unleashed a fierce strike which was denied by the crossbar.
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