Rajoy was reacting to comments by Tsipras on Saturday, who said that during talks that earned Greece a four-month extension to its bailout, pressure from certain other European countries "had the character of blackmail" - pointing especially to Spain and Portugal.
"Conservative forces (in Europe) tried to set a trap for us, to drive us into financial asphyxia," the 40-year-old Greek premier had said.
Speaking Sunday to a meeting of his conservative party, Rajoy fired back in the first out-in-the-open clash between Tsipras and another European leader.
"We are not responsible for the frustration created by the radical Greek left, which promised the Greek people things it knew it couldn't hold to," Rajoy said.
He noted that Tsipras's hard-left Syriza party had tried to lay the blame for Greece's problems on Spain and neighbouring Portugal.
"Looking for an external enemy is a way we've already seen many times in history... That doesn't solve problems, it aggravates them," Rajoy said.
"The only solution is to get serious," he advised the new Greek leader.
Both Madrid and Lisbon have filed official protests against Tsipras's comments with Brussels, with Portuguese officials also firing back.
Antonio Costa, spokesman for the ruling centre-right Social Democratic Party called Tsipras' allegations "totally absurd" in addition to being "grave, lamentable, and false."
Costa described the charges as being "sad coming from a leader who should be rising to assume his responsibilities," and said that statements "can not be justified by the internal difficulties Syriza is going through."
In his earlier comments, Tsipras claimed Greece had came up against "an axis of powers led by Spain and Portugal" that tried to scupper the negotiations to "avoid internal political risks."
"These powers do not want the Greek example to influence other countries, especially in the perspective of elections in Spain," this year, Tsipras said.
His remarks were seen as a reference to the rise of anti-austerity parties in Spain and Portugal, which have been buoyed by Syriza's arrival to power.
A Greek governmental source insisted on Sunday that Tsipras had a responsibility "to explain to the Greek people the details after crucial Eurogroup negotiations."
The positions of the European governments were no secret, he added.
"The Greek government doesn't class European countries and citizens as friendly or rivals. It doesn't look for enemies abroad but for solutions at the European level... Bad interpretation of the Greek PM's comments don't aid that dialogue."
In Spain -- which unlike Portugal did not receive a full bailout, but whose banks got emergency support in 2012 -- new anti-austerity party Podemos, a close Syriza ally, is leading polls ahead of general elections expected later this year.
In Portugal, meanwhile, opposition Socialists have echoed refrains by Syriza and Podemos in accusing ruling conservatives of failing to resist excessive "diktats" coming from Berlin.
Despite the official protests lodged over Tsipras' accusations, however, government officials in Spain confided they don't believe Brussels will take action, even if authorities there object to comments coming from Greece as much as Madrid does.
"I don't think the Commission will issue a public rebuke," the source said, noting that "in this very sensitive case, the Commission's role is to be the intermediary, not to divide."