Fleet boss Liam Daish was heartened by his players' display even though they didn't take any points from the game: "If they show me that sort of spirit for the rest of the season we will be okay," he said. "We regroup on Monday and will go again at Grays on Tuesday evening. Today was a setback, but it's a long season."
Fielding seven new signings Fleet settled quickly and dominated the first 40 minutes.
City took the lead against the run of play a minute before the interval, when a long clearance downfield was chased by Lee Phillips, who shrugged off Scott Gooding's challenge and slotted home on 44 minutes.
The goal was a setback for the Fleet, playing their first game as a full-time club in the Conference and in the second half Exeter took control of the game, but the home side still managed some good strikes on goal.
A Jimmy Jackson drive sailed inches over the bar on 62 minutes, but Paul Jones had to dive full length to deny Jackson a minute later.
Substitute Les Afful lasted only 31 minutes, being given a straight red card from referee Ray Lee for a challenge on Danny Slatter on 55 minutes.
Six minutes later Fleet were reduced to ten men when Ross Smith was adjudged to have pushed Jon Challinor in the back and Smith took the long walk to the dressing room before Phillips stepped up to score from the penalty spot.