Russell's departure, aided by two medics, from Sunday's 39-16 win is a cause for concern as Scotland prepare to face South Africa and Samoa.
"I'll need to talk to our medical boys; he seems to think it's not too bad," said Cotter of the Glasgow player.
"But we'll have a look. It's 24 hours before you have a decent idea."
Duncan Weir is likely to be the favourite to replace Russell should he not recover in time to face the Springboks next Saturday.
Weir came on for his stricken Glasgow team-mate at Elland Road, and scored the last of five Scotland tries after they trailed the Americans 13-6 at half time.
It was their second bonus-point victory of the tournament, following a 45-10 triumph over Japan on Wednesday, ensuring they top Pool B.
"We had opportunities in the first half and we were probably a little unsettled," added Cotter.
"They are a big, powerful side and they had us going backwards on a couple of occasions.
"We roughed and toughed it out four days after Japan so we're happy with the result, and we've got six days now to get ready for South Africa, so it doesn't get any easier."
Cotter is also awaiting injury news on back-row Grant Gilchrist, who went off injured in the first half.
The impact of replacements introduced after the interval aided Scotland's quest for dominance and dynamism, with WP Nel and Matt Scott particularly impressive.
"The players came in and gave us fresh legs and kept the intensity up," said Cotter.
"In a four-day turnaround, players coming in and fitting into a difficult situation like that is not easy, but these guys have worked hard to have that team cohesion and be able to slot in and out of positions and we'll need that going forward."
Scotland head coach Vern Cotter is unsure how long stand-off Finn Russell will be sidelined for with the injury that forced him off against the USA.