It was a desperately poor first half on a rotten pitch but Aldershot looked more likely to score, especially from set plays and corners.
Asa Hall saw a header hit the crossbar just seconds after Danny Hylton's effort had been saved by home goalkeeper Artur Krysiak.
Exeter's best chance fell to Jamie Cureton, but the ball got stuck under his feet when through on goal and in the end his shot was easily saved by Jamie Young.
Troy Brown headed over the bar as Exeter failed to clear a corner and Oliver Risser's fierce volley was well held by Krysiak.
City barely posed a threat but they did have the ball in the net only for Guillem Bauza to be flagged offside.
Aldershot were happy to play for time as the minutes ticked by and Exeter lacked the quality to break them down, despite seeing more of the ball.