Minutes after Stoke’s Tommy Smith had been shown a straight red card in the 85th minute for a lunge on Claudio Gomes, Potters coaches Dean Holden and Rory Delap plus Reds assistant Laumann were also red carded following a mass touchline brawl involving staff and players in the dying seconds.
The governing body have now investigated the footage and deemed that Eckert will be banned from the touchline for three matches, with Laumann handed a two-match punishment.
Eckeet has been handed a £2,750 fine and Laumann has been fined £2,500.
Meanwhile, Barnsley have been fined for £8,000 for their part in the melee, with Stoke issued with a £10,000 penalty with both clubs failing to ensure that players and staff conducted themselves in orderly fashion and refrained from behaving properly, according to the FA.
Holden and Delap have been handed one-match bans and fined £2,000 and £1,800 respectively after being deemed to have conducted themselves in an improper manner. Delap was also seen to have behaved in a manner which constituted as violent conduct.
The written reasons will be revealed in due course.
Speaking shortly after the game had finished, Reds head coach Markus Schopp said: "It all started with the Smith red card I think. The Stoke staff weren’t happy.
"It was an unnecessary situation, but I didn’t see too much of it.
"Maybe we should have been a bit more quiet, but the Stoke staff had been shouting at ours.
"There had been arguing after the player had been sent off."
It represents the second punishment which the Reds have received retrospectively so far this season.
Defender Liam Kitching was handed a three-match ban from the governing body after footage was reviewed of an altercation with Birmingham City substitute Chuks Aneke late on in the 1-1 draw at Oakwell on August 28.
Upon inspection of video evidence - the FA deemed the incident worthy of a violent conduct charge and a three-match ban.