Moscow (CNN) When President Donald Trump and President Vladimir Putin shared a phone call the weekend after Trump's inauguration, Russian news media delighted in covering every detail in near wall-to-wall coverage.

The optimism in Russia since Trump's victory has at times seemed tangible. So how extraordinary, then, that Trump's remarkable 75-minute press conference has been barely mentioned on Russian television.

Further to this, a Kremlin spokesman said Friday that Russia had "more important things" to do that watch the Trump event on Thursday.

Is the new friendship between the two superpowers already over?

Russian optimism dissipates

Ever since he won the Republican nomination, many suspected Trump to be Putin's preferred occupant of the White House.

JUST WATCHED Trump discusses recent Russian provocations Replay More Videos ... MUST WATCH Trump discusses recent Russian provocations 01:46

This is hardly surprising: during the Obama years, relations between Moscow and Washington went from bad to worse for a number of reasons -- from Russia's annexation of Crimea and military activity in eastern Ukraine to its backing of Syrian President Bashar al-Assad, to its reported interference in the US election.

Under President Barack Obama, the US strongly condemned each of these acts, and in the case of Crimea placed sanctions on Russian individuals and businesses, the desired effect being to hurt the Russian economy.

A Hillary Clinton presidency would have been at best an extension of Obama's policy; at worst, she could have been even more of an anti-Russia hawk than Obama.

In Trump, the Moscow establishment saw a man who might be open to a thaw in the relationship between the two powers.

But in the last few days, a sense of disillusionment has descended upon Moscow and the sense of Russian optimism following Trump's victory has somewhat dissipated.

'No rose-colored glasses'

JUST WATCHED NATO's increasing close calls with Russia Replay More Videos ... MUST WATCH NATO's increasing close calls with Russia 02:59

Only recently, the early days of the Trump administration were being covered in great detail on Russian television. Indeed, not long after his inauguration, the Russian news agency Interfax released a report saying that for the first time since 2011, Putin was not the most mentioned man in Russian media: that honor went to Trump.

More vocal criticism of the new US President is also appearing in Russian newspapers and from some Russian politicians.

This is translated from Friday morning's Komsomolskaya Pravda : "... one cannot but pay attention at president Trump's self-contradicting [or mutually exclusive] evaluations, which he made for NATO during the elections and today. Trump called the alliance outdated and useless. But less than two months after Trump settled into the Oval Office he expressed the full support of NATO. As they say, there's no way to understand the US president's real position without being drunk."

It's hard not to feel as though the man Putin might be hoping to call a friend has fallen from grace in the eyes of the Russian people.

JUST WATCHED Russians rush to buy US homes after Trump win Replay More Videos ... MUST WATCH Russians rush to buy US homes after Trump win 02:04

For their part, the Russians are claiming that they never harbored "excessive illusions," over how ties would develop.

Kremlin spokesman Dmitry Peskov told Russian media in a conference call on Friday morning: "Regarding the illusions and disillusions, I would like to remind that you over the period of the last few months, we kept saying that we've never worn rose-colored glasses or cherished excessive illusions. So we have nothing to be disappointed about."

There might be something to this. While many in Russia welcomed Trump's victory, this optimism was largely due to things that Trump said about Putin before taking office. It is certainly true that Trump has been louder in his praise (not to mention softer in his criticism) of Putin than vice versa.

Trump's change in tone

But the dramatic change in tone from Trump himself will certainly have been a blow to Putin. Only two weeks ago, Trump was implying to Bill O'Reilly that the US was in no position to preach to Russia. This week: " Crimea was TAKEN by Russia during the Obama administration. Was Obama too soft on Russia?"

The confusion of the last week and the mixed messages from Washington may have been enough for experienced heads in Moscow to stop holding out hope of Trump following through with any kind of thaw.

JUST WATCHED Trump campaign aides had contact with Russia Replay More Videos ... MUST WATCH Trump campaign aides had contact with Russia 01:49

Some will calculate that the last few days may have made Russia too poisonous politically for any US president.

Some in Moscow clearly believe that Trump is being forced to act against his better instincts.

In the wake of Michael Flynn's resignation following an intelligence leak concerning the contents of his conversation with the Russian Ambassador to Moscow, Konstantin Kosachev, the current chair of the Foreign Affairs Committee of the Russian Federal Council, wrote that "either Trump has not gained the required independence and subsequently (and unsuccessfully) is being backed into a corner, or Russophobia has already infected the new administration from top to bottom."

If information is being leaked with the intention of undermining any olive branches being offered to the Kremlin, it's clear that earlier Russian optimism was misplaced. Couple this with Defense Secretary James Mattis saying that the US was not "in a position right now" to work with Russia on any military matters, and the situation looks bleak from the Kremlin's point of view.

Now might be a politically sensible time for Russia to move away from the idea of a closer relationship between the two capitals. Russia is not used to this level of chaos in Washington. Putin may not have liked Obama, but at least he knew where he stood.