Both sides’ work rate could not be questioned throughout but, ultimately, the lack of cutting edge on show in the final third meant honours were even.
The Shrimps made one change to the starting XI beaten at Portsmouth a week earlier.
Scott Wootton was ruled out through the injury he sustained at Fratton Park, as was his second-half replacement, Ryan Delaney.
In came Ryan Cooney with Ryan McLaughlin switched from full-back to the right-hand side of a back three.
With fog circling the ground, it was Morecambe who were first to show going forward as Adam Phillips glanced a header narrowly wide from Cooney’s cross.
However, as the game began to settle down, the visitors got into proceedings and could have netted twice within a minute just past the quarter-hour.
The first occasion saw the ball threaded through to Cian Hayes, who was denied by a fine last-ditch challenge from Anthony O’Connor.
Seconds later, Ged Garner played Shayden Morris in behind Liam Gibson but, one-on-one with Kyle Letheren, his shot was kept out by the keeper.
With chances proving at a premium, Morecambe had a good opportunity when Cole Stockton was fouled 20 yards out, only for Phillips’ free-kick to hit the top of the defensive wall.
Another opportunity fell Stockton’s way on 39 minutes, collecting Phillips’ pass but curling an effort over from 18 yards.
There was still time for Letheren to hold a Danny Andrew shot and Greg Leigh to have an effort blocked at the other end before the break, after which conditions began to worsen.
Both sides huffed and puffed in the early stages with neither keeper forced into serious action.
Morecambe freshened up their attacking options, introducing Jonah Ayunga for Jon Obika almost an hour into his first home appearance of the season.
Toumani Diagouraga was also brought on, replacing McCalmont, as the Shrimps sought a breakthrough.
Nevertheless, it was Town who enjoyed a spell in the ascendancy with the lively Hayes seeing an effort blocked and Letheren holding Garner’s shot from distance.
Aaron Wildig came on for Phillips, a move that almost paid dividends on 78 minutes.
A ball in from the right found Ayunga, whose shot was blocked, the ball eventually falling to Wildig who snatched at his effort.
Hayes had another attempt blocked before Morecambe had a great chance to score in the 88th minute.
Stockton was played clear down the left-hand channel and, having worked the ball back onto his right foot, saw his shot kept out by Town keeper Alex Cairns.
Then, as the four scheduled minutes of added time drew to a close, Fleetwood were awarded a free-kick 25 yards out.
Andrew, usually deadly from those positions, chanced his arm but saw his effort kept out by Letheren before the final whistle sounded seconds later.
Morecambe: Letheren, R McLaughlin, O’Connor, Gibson, Cooney, McLoughlin, McCalmont (Diagouraga 64), Leigh, Phillips (Wildig 76), Stockton, Obika (Ayunga 56). Subs not used: Andresson, Jones, Mensah, Gnahoua.
Fleetwood Town: Cairns, Johnston, C McLaughlin, Clarke, Andrew, Matete, Lane, Biggins (Camps 81), Hayes, Morris (Conn-Clarke 74), Garner. Subs not used: Crellin, Edmondson, Clark, Boyle, Bird.
Referee: Christopher Pollard.
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