The ECB surprised markets on Thursday by refusing to lower its main interest rate in response to the coronavirus pandemic. Lagarde appeared to make matters worse by noting that the institution was "not here to close spreads" between the borrowing costs of member states.
Her words contributed to a record 17% drop on the Milan exchange and a spike in the yields of Italian bonds.
"Let me express my disgust, horror and shame for what is happening in Europe," Italian far-right leader Matteo Salvini said.
"The only help from Europe was to bring down the stock market and drive the spreads crazy. Yesterday, the Italians lost 68 billion euros in savings," he claimed.
"We will consider the possibility of asking for economic compensation." The Milan stock exchange followed global markets higher on Friday and was back up 17.7% at around 1230 GMT.
But the former IMF chief's comments made an impression with even more moderate politicians in Rome.
"President Lagarde objectively made a mistake yesterday," former Italian prime minister Matteo Renzi was quoted as saying by Italy's AGI news agency.
"I hope it is only a mistake of communication, not a change of line with respect to (former European Central Bank head Mario) Draghi's management," Renzi said.
Lagarde appeared to try to walk back her comments in an interview following the ECB press conference.
The ECB is "fully committed to avoid any fragmentation in a difficult moment for the euro area," she told CNBC.