Ryan Harley grabbed a brace as Leeds' advantage at the top of the table was cut to three points by Norwich City.
But Grayson said: "We have only lost two games all season and that is not a bad statistic.
"Any defeat is disappointing but we are still in a decent position in the league.
"Credit to Exeter, they put us under pressure and we didn't get a break in front of goal.
"We knew it was going to be difficult conditions and we warned the players about that before the game. But we didn't start the game well and we were still in the dressing room for the first 15 minutes.
"We improved after the break but we didn't get a break in front of goal. We should have played percentage football but we didn't. Exeter did and credit to them."
Paul Tisdale's home side laid siege to the Leeds goal in the opening stages and Harley headed past Casper Ankergren for the opener.
It could have got even worse for the visitors but Ankergren spared Leigh Bromby's blushes when he tipped the defender's sliced clearance over the bar.
Leeds were second best in the opening half and the nearest they came followed a mix-up in the City defence between Richard Duffy and Paul Jones.
Striker Lucianno Becchio's ambitious long-range strike summed up Leeds' frustration in being unable to break down a well-drilled Exeter side.
Grayson's side improved after the break as he switched to a
Andy Hughes fired at Jones following a through ball from Robert Snodgrass and 20-goal Jermaine Beckford headed over the bar and was twice thwarted by Jones.
Leeds threw caution to the wind but Bradley Johnson could not find a way past Jones.
Exeter City: Jones, Duffy, Taylor, Edwards, (Sercombe, 71); Golbourne, Harley, Russell, Cozic, Tully; (Dunne, 86), Stewart, Stansfield (Logan, 90). Unused substitutes: Marriott, McAllister, Saunders, Fleetwood
Leeds United: Ankergren, Bromby, Naylor, (Grella, 75), Kisnorbo, Hughes; Snodgrass, Kilkenny, Doyle (Howson, 66), Johnson; Becchio, (Gradel, 71), Beckford. Unused substitutes: sed: Jones, Michalik, White, Crowe
Referee: G Scott (Oxfordshire).
Man of the match: Neil Kilkenny.
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