His top diplomat offered a similarly grim assessment from the other side of the globe after meeting with Russian President Vladimir Putin in Moscow.
The meeting Wednesday, announced by Putin spokesman Dmitry Peskov, comes hours after Tillerson faced his Russian counterpart Sergey Lavrov in a tense encounter. He said "it would be a fantastic thing" if the two nations got along better but cautioned that "it may be just the opposite".
Could Syria have launched the chemical weapons attack with Russia's advance knowledge?
"The level of trust at the working level, especially at the military level, has not become better but most likely has degraded", Putin said in an interview broadcast Wednesday by state television channel Mir.
The White House has accused Moscow of trying to cover up Assad's use of chemical weapons after the attack on a rebel-held Syrian town last week killed 87 people last week.
The Moscow news conference came after Putin met Tillerson for the first time since Trump took office.
The diplomats know each other well from Mr Tillerson's days as Exxon Mobil chief executive. Putin had even granted Tillerson with a friendship honor.
Russian Deputy U.N. Ambassador Vladimir Safronkov shows his hand to vote against a resolution condemning Syria's use of chemical weapons, Wednesday, April 5, 2017, at U.N. headquarters.
Lavrov blasted US claims that it has "irrefutable evidence" of election interference. He also said war-crime charges could be possible "the longer time goes by". "I do not know who saw them". "In order to overcome such obstacles we will need to imply weighty efforts on condition that our USA colleagues will meet them".
Russia, meanwhile, intervened in the civil war on Assad's side in 2015 and has troops on the ground, which it says are advising government forces.
The Trump administration says Syrian President Bashar al-Assad ordered the attack.
In what was effectively an ultimatum, Tillerson on Tuesday said that Moscow must calculate the costs of remaining an ally of Assad, the Iranians and Lebanon's Shiite militia Hezbollah.
Looking at the resolution's supporters sitting around the horseshoe-shaped table in the Security Council, he said: "You are afraid of an impartial investigation" that the Syrian government was being blamed for chemical weapons attacks carried out by extremists.
Tillerson arrived in Russian Federation with less ammunition than Washington and London had hoped he would have in his bid to convince Russian Federation to abandon its support for Assad.
The civil war is separate from the US-led effort against the Islamic State group in the north of the country.
His visit came as US criminal investigators and members of both the Senate and House of Representatives intelligence committees are investigating details of the USA intelligence community's conclusion that Putin meddled in last year's US election.
Tillerson, a former oil executive, might once have looked like the flawless envoy to mend strained ties, having worked closely with the Kremlin while negotiating deals for energy giant ExxonMobil.
But Tillerson said the Ukraine remains the largest obstacle to improving the U.S.
Lavrov said it was important for Russian Federation to understand Trump's "real intentions". "We consider it of utmost importance to prevent the risks of replay of similar action in the future".
Putin accused the Trump administration, in turn, of fabricating the evidence in the attacks to create a confrontation, and saying the US accusations reminded him of the events of 2003, when Security Council representatives claimed chemical weapons were discovered in Iraq.
Finally, the New York Times reports that Trump's rapidly changing positions on Syria, Russia, and a host of other global issues are giving leaders around the world "geopolitical whiplash". "I think it's very bad for Russian Federation".
Trump's relations with Russian Federation are also a domestic issue, as US intelligence agencies have accused Moscow of using computer hacking to intervene in the election to help Trump win.
And Putin, who US intelligence agencies say tried to help Trump get elected, insisted that relations with the USA had only gone downhill since Trump took office in January.
Lederman reported from Moscow.