A number of clubs are waiting to hear their sanction for breaking the European body's rules on spending, but Platini said although tough penalties would be issued, the maximum punishment of exclusion from European competition would not be applied this time.
Manchester City and Paris St Germain are understood to be among around 20 clubs dealt with by UEFA's Club Financial Control Board (CFCB) earlier this month, with those facing action to be announced on May 5.
Platini told Le Parisien newspaper that the maximum penalty would not be applied.
Platini said: "If you are expecting blood and tears, you will be disappointed. There will be some tough things but I think there will be no exclusions from European competition.
"I think that significant sanctions will affect the big clubs. We will go through with this."
Qatar-owned PSG are the club under most scrutiny after they wiped out their losses with a huge and back-dated sponsorship deal with the Qatar Tourist Authority.
Platini said he was unsure if that "innovative" sponsorship deal played by the rules.
He added: "I will say simply that Paris St Germain's financial model is distinctive and atypical. That image contract with the QTA, the tourism office of Qatar, is innovative, that's all I can say.
"But is it viable? Is the value of the contract correct? These are questions that the experts must decide."
Manchester City, who have lost £149million in the past two seasons, are also at risk but have been working with UEFA to try to comply with the FFP rules.
The CFCB panel will have four options open to them - to dismiss the case; to agree a settlement with the club effectively putting them on probation; to issue a reprimand and fine of up to 100,000 euros; or in serious cases to refer the club to the adjudicatory chamber.
That second disciplinary panel can issue a number of sanctions, from a warning to points deductions, a salary cap for the European squad, withholding revenues or exclusion from European competition.
- Paris St Germain
- Manchester City