Victory for Inverness against Dundee United would spell the end of County's hopes of making the Europa League before they take on Motherwell on Sunday.
But few expected the Dingwall side to be in the top six in their debut top-flight season and Adams will watch neighbours Caley Thistle take on Dundee United with the knowledge that his team have over-achieved regardless of the fate of their European challenge.
Adams said: "We've still got an opportunity, we play after Inverness and St Johnstone and if Inverness win and St Johnstone don't, then they're in Europe.
"It's in Caley Thistle's hands and has been for the majority of the season.
"We know going into our game what we have to do after Caley Thistle and St Johnstone will have played, and it might be impossible.
"However, after Saturday it might mean we'll need four points, it might mean we'll need six points. But we'll just see what happens with both teams."
Adams, whose team took points off Celtic for the third time last weekend, added: "Taking a point against the champions was excellent last week and going unbeaten against them at home over the season is also good, who would have believed that at the start of the season?
"We've had a fantastic season and we're just delighted, it looks like we're going to cement fifth position and perhaps go as high as third."