The pair, named in Italian media as former director general Paolo Cipriani and his former deputy Massimo Tulli, were dismissed in 2013 and last year handed suspended jail terms for minor breaches of rules to prevent money-laundering.
In a statement, the Vatican press service said the Civil Court of the Vatican City State found the two former officials at the Institute of Religious Works (IOR), as the Vatican bank is known, liable for mismanagement.
The pair must "compensate IOR for the resulting damages, the court added. The IOR started the civil liability action in September 2014 and Tuesday's statement underlined "the significant work of IOR senior management over the last four years to transform" the organization as well as its "continuing commitment to strong governance, transparency to its operations and its determination to meet best international standards."
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The Vatican bank added that the ruling "confirms IOR's will to pursue by judicial proceedings any misconducts carried out to its detriment, no matter where and by whom."
The statement did not say what sums the two former managers might have to pay by way of compensation.
The IOR has some 15,000 clients, mainly connected with the Catholic Church, and manages assets of some 5.7 billion euros. The Vatican's bank became notorious after the 1982 death of Roberto Calvi, known as "God's banker" because of his links to the Vatican, whose corpse was discovered hanging from Blackfriars Bridge in London.
Prosecutors believe it was a mafia killing linked to money laundering via the bank. That and other scandals prompted a clean-up in recent years, first under Pope Benedict XVI and then under current pontiff Pope Francis with some 5,000 bank accounts being closed.
A further blow to the bank's reputation came in November when deputy director Giulio Mattietti was suddenly dismissed months after Vatican auditor general Libero Milone resigned, the latter saying he had been forced out by opponents of modernization of the city state's financial system.