The Shrimps, who included new signing Ritchie Sutton in their new look three-man defence, restricted the home side to few chances and came close to winning the game themselves in the second half.
Exeter had the better of the first half but they seemed to lack a goal threat up front after selling 16 goal Jayden Stockley to Preston North End this week and that suited the Shrimps who had so often been victim of Stockley’s strikes.
Another former North End man, Lee Holmes, looked to be Exeter’s biggest threat but without Stockley to aim for the Shrimps’ defence was relatively untroubled.
Midfielder Nicky Law had the first chance and headed wide form 12 yards from Pierce Sweeney's cross before the Shrimps almost handed the Grecians the lead when Steven Old sliced a Craig Woodman cross inches past his own goal
Attacking right back Sweeney linked up well with Holmes and always looked a threat going forward and saw a well struck effort tipped onto the crossbar by Mark Halstead
Morecambe always looked dangerous themselves on the counter attack and Kevin Ellison headed narrowly wide from 10 yards after nipping in between two defenders to get onto a right wing cross.
The Shrimps had the better of the second half and looked the more likely to score.
On 63 minutes Oates was presented with a good chance on the edge of the Exeter box but flashed his half-volley over Pym’s crossbar.
Pym was to be the busier keeper in the second period as he made a fine flying save from another delicate Andrew Tutte free kick that was heading for the top left hand corner.
Jordan Cranston also forced the home keeper in a save before Exeter staged a late onslaught.
Old, Sam Lavelle and Luke Conlan all made fine blocks before defender Dean Moxey went close in injury time when he headed Craig Woodman’s left wing cross just wide as both sides had to settle for the point.
Exeter City: Pym; Sweeney, O’Shea, Moxey, Woodman; L Martin, Law, Collins, Taylor ©, Holmes (Bowman, 69); Forte (Jay, 77).
Subs not used: Hamon, A Martin, Tillson, Abrahams, Hartridge.
Booked: Moxey, Law
Morecambe: Halstead; Old, Lavelle, Sutton; Conlan, Cranston, Kenyon ©, Tutte (McKay, 86), Mills; Ellison, Oates (Mandeville, 69).
Subs not used: Szczepaniak, Campbell, Mendes-Gomes, Hedley, Hawley.
Attendance: 4,113 (62 away)