The opposition and Kurdish groups had boycotted the congress, held just days after a ninth round of United Nations-led talks in Vienna failed to yield progress towards ending Syria's devastating conflict.
The West views Russia's Syria peace efforts with suspicion, concerned that Moscow is seeking to sideline the UN process.
But the US acting assistant secretary of state, David Satterfield, said Wednesday that the fallout had been limited.
"We got in the end a communique which validated the UN role," Satterfield said before Tillerson's meeting in Amman.
"So this game, this theatre that was Sochi... finally came out in a way that did no damage."
Despite Moscow insisting Syrian society would be fully represented at Sochi, almost all of the 1,400 delegates were pro-regime.
They agreed to set up a commission to re-write the country's post-war constitution.
About 150 Syrian civil society groups accused the UN of rewarding Russia by dispatching its special envoy Staffan de Mistura to the congress.
Syria's war has killed more than 340,000 people and displaced millions since it began in March 2011 with the brutal repression of anti-government protests.
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