They have also received mixed news on the injury front with three players close to a return, but another beginning a long spell on the sidelines.
Parcell was given a one game penalty notice over an incident as he moved in to make a tackle in the first half against London and received a similar punishment for a second offence, on a kick-chase, after the break.
The Rugby Football League’s disciplinary committee has the power to increase bans if they decide an appeal is “unreasonable”.
Rhinos’ interim coach Richard Agar said: “We won’t appeal it.
“We don’t for a minute think it was deliberate, but the definition of the charge is about duty of care and twice he has run into the ref’.
“He has his eyes very firmly on the [London] man in the first one and the second time his eyes are on the ball.
“However, the feedback we got from the match review panel was they feel he had sufficient time to avoid contact and it was his duty of care.
“So, we were pessimistic about getting a not guilty.”
Nineteen-year-old England academy hooker Corey Johnson is an option to replace Parcell on the bench in the forthcoming games at Wakefield Trinity and home to Wigan Warriors.
“He will come into the mix,” Agar said.
“I’ve got his [academy] game from the weekend to have a look at and I am a really big fan of him.
“He distributes the ball well, he is decent around the ruck and he has a big engine on him, but defensively we need to know he can hold his own against a big, strong pack.”
Meanwhile, prop Nathaniel Peteru suffered a fractured eye socket against London and Agar reported: “The first indications are he will be out for six to eight weeks.”
In better news, Agar said Tui Lolohea (ankle), Konrad Hurrell (hamstring) and Brett Ferres (knee) are all set to return against Wakefield on June 7 and long-term casualty Stevie Ward (knee) will be “a couple of weeks” after that”.
Carl Ablett, who has not played this year, has suffered a setback in his recovery from two ankle operations.
The veteran forward had hoped to be available for selection this month.
Dom Crosby, who has also yet to feature this term, has undergone another knee operation, but is now walking without a leg brace.
Jamie Jones-Buchanan suffered a hamstring problem in the defeat at Salford Red Devils on May 3 and was expected to be sidelined for arounds six weeks.