Sean O'Driscoll has vowed to produce a new vibrant Bristol City team after being relegated following defeat to Birmingham City.
Wade Elliott's first-half goal proved to be enough to condemn the Robins to defeat and send them down into League One.
City manager O'Driscoll is resigned to a summer of losing many of his highest-paid players, but is relishing the challenge of turning their fortunes around after a 1-0 home defeat by Birmingham confirmed their relegation.
"That result and performance sums up the club's season," said O'Driscoll. "The players gave it everything in the second half, but couldn't take the chances.
"We needed promotion form when I took over and that is not easy with the same group of players when you are bottom of the table.
"There will be changes in the summer and we will do our best to provide a vibrant young team, who can take the club up again.
"It is no good having an academy if you are not ready to use the players it produces. The fans have stuck behind us brilliantly and we want to reward that."
First-half goals from Joe Bryan and Curtis Nelson gave the visitors a two-goal half-time cushion and, although Guy Branston put through his own net 12 minutes after the break, Plymouth held on for three precious points.
Argyle started well and had already created two chances before Bryan put them in front with a brilliant curling shot from the left side of the box in the 21st minute.
The visitors increased their lead five minutes later when Chesterfield failed to get the ball away and Nelson pounced to fire into the roof of the net from close range.
The hosts had offered little in the first half but they were handed a lifeline in the 57th minute when Branston turned a low cross into his own net.
They had plenty of possession but could not find a way through a stubborn defence and Andres Gurrieri missed a good chance to score a third late on.