Russia's presidential spokesman Dmitry Peskov did not expect much to change as a result of the high-level staff changes in the US administration.
"It's hardly possible to fall below the floor, so it is unlikely things will get any worse in this regard."
"In any case, there of course remains the hope of a constructive and sober approach to bilateral ties. There is always this hope," Peskov said at a press briefing.
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US President Donald Trump announced he had sacked Mr Tillerson as Secretary of State on Twitter on Tuesday.
In a press conference shortly after being sacked, Mr Tillerson warned of Russia's "troubling behaviour and actions".
"Russia must assess carefully as to how its actions are in the best interests of the Russian people and of the world more broadly," he said.
"Continuing on their current trajectory is likely to lead to greater isolation on their part, a situation which is not in anyone's interest."
The US has accused Russia of actively interfering in the 2016 presidential election, stealing Democratic party communications and pushing out disinformation through social media, claims Moscow denies.
Tillerson's replacement Mike Pompeo said in his previous role as CIA director that the agency had observed Russian activity to influence the next US election cycle, the November mid-terms.
