Reading manager Nigel Adkins was left to rue a poor start to the second half after a 2-1 defeat by Norwich almost confirmed their relegation.
The Royals were undone by two goals in two minutes at Carrow Road and, despite pulling a goal back late in the game, they were unable to recover.
Adkins' side could now be consigned to the Championship before they play QPR next Sunday if results go against them.
He told Sky Sports: "I thought we did well first half but it was disappointing how we started the second half.
"We said it was important how we dealt with the balls they play into the box and the physicality and we did it well for the most part.
"But for that 15-minute spell we just couldn't deal with them - that led to the two goals."
But, despite their predicament, Adkins vowed there would be no let-up in the work rate of his players.
He continued: "At the end of the day we've lost a game of football. We're in a poor position in the league. We can look at it and take positives from it but we've lost.
"We carry on. The players worked hard and showed a lot of endeavour and we'll keep working hard.
"We'll analyse this game, learn the lessons from it and get ready for the next game."
Agard applied the deft close-range finishing touch after skipper Johnny Mullins headed down Joe Skarz's free-kick into the six yard box.
Lee Frecklington missed a gilt-edged opportunity to fire United just before half time when he was denied by a superb Jake Cole save.
Ben Pringle's angled 45th minute header across the area found Frecklington on the right but his shot was brilliantly turned around the post by Argyle's keeper.
Argyle's best first half chance came early on as Andres Gurrieri's third minute corner caused a goalmouth scramble, eventually cleared by Mullins.
Rotherham started the second half brightly with striker Alex Revell going close in the 47th minute and Agard heading wide from Pringle's cross minutes later.
Argyle responded with striker Reuben Reid flashing a stooping header inches wide from Onismor Bhasera's pinpoint near-post cross from the left in the 53rd minute
Reid should have scored from Bhasera's next cross, a minute later, but fired high and over from 12 yards.
The home side dominated much of the first half as Jamille Matt, Gareth Evans and Ryan Crowther all enjoyed chances to open the scoring.
But Chesterfield grabbed the lead against the run of play when substitute Armand Gnanduillet headed home Conor Townsend's corner in the 44th minute.
And from the restart the visitors doubled their tally, Richards on the end of a long ball before firing a stunning 25-yard effort which was too good for Scott Davies - capping a stunning finish to the first half.
Richards then made it three-nil just after the hour mark, lashing home the rebound after Davies saved Sam Togwell's goalbound effort.
Andy Mangan's first goal since August gave the home side hope, a perfectly timed run to get on to David Ball's defence-splitting pass and a cool finish.
Had Mangan found the net again, first shooting wide from 18 yards before then looping the ball over the bar from close range, Fleetwood might have set up a grandstand finish but it was not to be.
As it was Chesterfield stood firm and are certain to finish above the home side, who are winless in five, but Paul Cook's side cannot now catch Bradford in the fourth and final play-off place.
