Nottinghamshire say they "respect the ruling" which resulted in them losing their place in the Twenty20 Cup quarter-finals.
Monday's disciplinary commission, which met in Taunton, awarded the place to Glamorgan as the best third-placed team after Yorkshire were docked the two points which had initially been credited to Nottinghamshire.
The Welsh county will now compete with Durham for a place in finals day at the Rose Bowl a week on Saturday, where the two successful semi-final teams will be guaranteed a shot at a £2.5million jackpot in India.
"It has been a very challenging process for all involved but we accept the findings of the panel and wish all sides well after what has been a very difficult week for cricket," said Derek Brewer, chief executive at Trent Bridge.
"When the original ruling was made, we were mindful that there would be an appeal and that any thoughts of a place in the quarter-finals were perhaps premature.
"We made our representation to the panel as did the other counties involved and although disappointed, we respect the ruling.
"There is no mechanism for appeal and with the finals day at the Rose Bowl less than two weeks away, it is important that a line is ruled under this issue and we pursue success in the LV County Championship and NatWest Pro40."
Yorkshire had gone into yesterday's disciplinary commission appeal in Taunton fighting expulsion from the competition.
Although they claimed a moral victory, after winning the right for their nine-wicket win over Nottinghamshire to stand, they were still deducted the two points for fielding ineligible teenager Azeem Rafiq.
The original decision made at Old Trafford last Thursday awarded those two points, and a quarter-final place, to Nottinghamshire.
But the amendment, made by a panel chaired by David Gabbitass, means that Glamorgan, as one of the best two third-placed teams, progress.
The date of their tie with Durham at the Riverside is expected to be confirmed on Tuesday or Wednesday.