The visitors led 2-0 at half-time in the Southern Combination League Premier Division match but Chamel Fenelon’s excellent free kick got a goal back on the hour.
Mavericks pressed for an equaliser but Chichester sealed their win from the penalty spot seven minutes from time.
Geary said: “I thought we were unlucky. We didn’t have a great first half but had a couple of good chances before they scored right on half-time to go in 2-0 up.
“Chamal scored a really good free kick and then it was all us. We had some good chances, before they got what I thought was a really harsh penalty. The ball has hit Jack Punter’s hand but it’s been kicked at him from no distance at all and he’s had no time to move.
“I thought we probably deserved a point from the game but we’ve just got to stop giving silly goals away as we leave ourselves with too much to do.
“Chichester are a good side but, at home, I feel we should be getting at least a point against them.”
United’s Owen Callaghan shot over from the edge of the penalty area, before Chichester took the lead on 32 minutes when Josh Clack’s cross was met by Scott Jones.
Mavericks’ Adrian Todd shot a one-on-one opening wide and Fenelon had an effort well saved, before Chi doubled their lead. United keeper Fraser Trigwell parried the ball out and Clack was on hand to drill the ball home from 12 yards.
Fenelon got a goal back with an excellent free kick on 60 minutes and Mavericks then had opportunities to get level.
George Rudwick got through but shot over and Chi keeper Anthony Ender denied Fenelon and Matt Hards.
The visitors sealed the points late on when Punter was adjudged to have handled a cross and Ellis Martin scored from the spot.
UNITED: Trigwell; Punter, Stideford, Hasan, Marsh; Todd, Nagle, Hards, Rose, Callaghan; Fenelon. Subs: Waller (Callaghan 60), Rudwick (Rose 74), Gritt (Todd 84), Wells.
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