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Chatham's FA Vase dream ended at the third round stage after they drew a blank against Flackwell Heath on Saturday.
The hosts also had skipper Jack Evans sent off late on as the Hellenic League leaders produced an excellent defensive display.
Chatham dominated the early possession in what was an open game until the first goal saw the chances more limited.
That said Chats had at least eight good openings in the first half only to trail at the break.
An early Evans free-kick hit the defensive wall with referee Nick Dunn waving away claims of handball.
Evans then connected with a deep Ryan Hayes cross but his header skimmed the top of the crossbar.
A fluffed clearance from Chats keeper Jordan Carey straight to Khalid Simmo saw the Heath winger drag his first-time shot wide as he aimed to score into an empty net from distance while Carey did well to hold Jack Taylor's low drive.
Evans made himself room inside the Heath penalty area but keeper Aaron Watkins pushed away his right-foot curler.
The goal arrived on 20 minutes The lively Simmo latched onto a loose ball 40 yards from goal and drove forward before cutting back onto his right foot and bending his shot beyond the reach of Carey.
Luke Rooney and Hayes both went close from distance while it needed a fine defensive clearance from Fikayo Ajayi to deny Simmo a tap-in for his second just before the break after promising play by Adam Thomas.
Chats nearly levelled in stoppage time as Watkins flapped at another Hayes delivery and then the keeper did well to turn behind defender James Essex's sliced clearance.
Chatham had a glorious chance to level eight minutes into the second half. Hayes, who had been switched to the left wing, fired a cross along the six-yard box but Bradshaw somehow failed to make any connection when a goal seemed certain.
Chats boss Scott Lindsey made a double change on the hour, surprisingly taking off Hayes, and one of the change - Andy Pugh - was quickly denied by the impressive Watkins.
Pugh then fired wastefully over and as timed ticked by you got the impression it wasn't going to be Chatham's day as they were continually faced with a wall of yellow shirts.
Frustration started to creep in for the home side and Evans, booked for a trip midway through the second half, was shown his second yellow two minutes from time by referee Nick Dunn.
Flackwell successfully ran the clock down and Dunn added a cautious five minutes of stoppage time, during which Chatham failed to create a clear-cut opening.
Chatham: Carey, Bodkin (Pilbeam 87mins), Ajayi, Robins, Lawal, Dickens, Hayes (Orji 62mins), Evans, Bradshaw, Rooney, Dalton (Pugh 62mins). Subs not used: Mills, McIlheron, Brown, Abioye.
Flackwell Heath: Watkins, Gray, Pryor, Mansfield, Essex, Ceesay, Baines, Taylor, Thomas (Touray 84mins), Howell (Eaton 90mins), Simmo (Lumb 89mins). Subs not used: Fraser, Burrell, O'Sullivan.
Referee: Nick Dunn.