Aironi and Treviso competed in the Celtic League for the first time in the 2010/11 edition of the tournament but the FIR announced last week that Aironi wouldn't be competing next year due to their financial problems.
Aironi are currently bottom of the PRO12 table having won three games this season. Their best win coming against rivals Treviso just before Christmas when they convincingly won the derby 27-13 for the first time.
Dondi explained that although there were plans to help put Aironi on the right tracks, the true extent of their finances meant the federation had to concede defeat.
"I am very sorry about Aironi," said Dondi. "But there was no other option.
"The federation cannot be a substitute for the sponsors and we have invested a lot already.
"Remember that we already pay 60% of the franchise's wages to players who can play for Italy.
"We were ready to pour in almost €3 million including a new coach who would have been available to Aironi and we would have given money to the Celtic League for Aironi's subscription.
"They however wanted other financial help and were speaking of another two and a half million, which wasn't possible."