Exeter chief executive Tony Rowe suggested Saracens should be relegated from the Gallagher Premiership as the defending champions vowed to fight their punishment for breaches of salary cap regulations.
Saracens were handed a 35-point deduction and fined more than £5million on Tuesday, although both sanctions will be suspended while the club - who described the action as "heavy-handed" - appeal against them.
Had the points penalty come into effect immediately, it would have left the team on -26 points after three games played in the current campaign.
Should the appeal fail and the original sanctions are upheld, the club are liable for the full £5,360,272.31 within 21 days of the decision under Premiership Rugby regulations.
Saracens chairman Nigel Wray said: "This is absolutely devastating for everyone associated with this amazing group of players, staff, partners and fans."
But Rowe, whose side have lost the last two Premiership finals to Saracens, does not feel the penalties go far enough.
"We, for a number of years, have suspected they've been infringing the salary cap," he told BBC Radio Devon.
"But I don't think the penalty is severe enough. You take away 35 points this year - they could still be in the semi-finals and could still end up at Twickenham (in the final)."
Putting forward an alternative punishment, Rowe added: "Relegation - in professional sport in America, if you're in breach of the salary cap you get thrown out completely."
Exeter lost last season's final by only three points and Rowe says he has been left with a "nasty taste".
"It's the management that have totally flouted the rules and regulations, which has enabled them to put a squad on the pitch that we couldn't match," he said.
"I feel a bit bitter about it because we were only just beaten. I'm not blaming the (Saracens) players, you can't blame the players.
"It leaves a bit of a nasty taste in my mouth. If you're in sport and you get beaten fair and square that's fine, but then to find out that your opponents have actually cheated, it's not good."
An independent panel led by barrister Lord Dyson found the club had failed to disclose payments to players in each of the 2016-17, 2017-18 and 2018-19 seasons, and had also exceeded the ceiling for payments to senior players.
No details have been revealed on the size of the undisclosed payments or the recipients, but Premiership Rugby's investigations were thought to have centred around Wray's involvements in companies such as VunProp Ltd (Mako and Billy Vunipola), Faz Investments Ltd (Owen Farrell), Wiggy9 Ltd (Richard Wigglesworth) and MN Property Solutions Ltd (Maro Itoje).
The panel was established after a nine-month Premiership Rugby investigation led to charges being brought in June. The panel upheld all the charges.
"It has been acknowledged by the panel that we never deliberately sought to mislead anyone or breach the cap and that's why it feels like the rug is being completely pulled out from under our feet," added Wray.
"We will appeal all the findings."
A separate statement from the club defended the use of co-investment arrangements with players, and stated that "PRL precedent already exists whereby co-investments have not been deemed part of salary in the regulations".
The club admitted some administrative errors had been made that led to some transactions not being disclosed to Premiership Rugby, and apologised for those errors.
However, they added: "It is the club's belief that the panel's narrow interpretation of the regulations is detrimental to player welfare across the league and is damaging the development of elite level rugby in the UK.
"Saracens is proud of its pioneering, innovative approach to player welfare, developing their talents and supporting their entrepreneurial spirit for life beyond rugby."
Director of rugby Mark McCall is due to attend the launch of this season's Champions Cup on Wednesday and will likely face further questions surrounding the sanctions, including the impact of such off-field issues for his playing squad.
Wednesday's event in Cardiff marks the beginning of a campaign that will see Saracens take on Munster, Ospreys and Racing 92 in Pool Four.
Saracens - founded in 1876 - have been the most successful English side of the past decade, winning three of the past four European crowns in addition to five Premiership titles since 2011.