Yossi Sarid, writing in Israel's Haaretz newspaper, said that the "lies" told about the reported visit to Russia "harm Israel's credibility".
Gil Hoffman wrote in the Jerusalem Post that the alleged cover-up was a sign of Netanyahu's "skewed" perception of threats to his position.
The previous day, the Yedioth Ahronoth newspaper and its main competitor, Maariv, ran the story under the identical headline: "Secrets and lies".
Confusion arose on Monday after journalists questioned officials about the whereabouts of Netanyahu, after his diary had been cleared for the day.
Nir Hefetz, Netanyahu's media adviser, had admitted he did not know where the prime minister was.
A statement claiming he was visiting a "security facility" was released later in the day by Major General Meir Kalifi, Netanyahu's military secretary, with local media reporting that he had toured a site used by the Mossad intelligence services.
Netanyahu's office moved to distance itself from the apparently false report as news of the Moscow trip leaked out.
"The prime minister was busy with confidential and classified activities," the statement said.
"The military attache, who was not in touch with the prime minister at that time, acted on his independent initiative in order to defend that activity, and did this through a statement that was sent to his media adviser with the best of intentions," it read.
Although it did not confirm the prime minister's whereabouts on Monday, media reports suggested a private plane had been booked to fly Netanyahu and news of the visit had been leaked by officials angry at not being informed.
Andrei Nesterenko, the Russian foreign ministry spokesman, when asked about the meeting, told reporters: "I am not saying yes or no, I am just saying I don't have any information."
Russia's Kommersant newspaper, citing a "highly placed source in the Kremlin," reported that it had confirmed the visit and speculated the talks had been on an extremely urgent matter "like Israel updating Russia on its intention to attack Iran".
Israel has previously indicated that it could be prepared to attack the Iran's nuclear sites if international sanctions fail to persuade Tehran to curb its atomic programme.
However, other media suggested that Netanyahu had been in Moscow in an attempt to persuade Russia not to hand over S-300 anti-aircraft missiles that it has agreed to sell to Iran.
The reported visit came after other media reports, which have been denied by Moscow, suggested that a cargo vessel intercepted by the Russian navy off Cape Verde last month was carrying S-300 missiles to Iran before it was detected by Israeli intelligence.