While in-form Caley Thistle were moving into second place in the Clydesdale Bank Premier League on Saturday with a 3-0 win over Hibernian, their Highland rivals were slumping to a 3-2 defeat at Motherwell despite taking the lead and then bringing the game back to 2-2.
After a solid start to their first season in the SPL, the Staggies are without a win in six games and boss Adams was particularly displeased with the concession of Nicky Law's strike a minute into the second half at Fir Park, calling it "idiotic" and "totally unacceptable".
Adams is looking for improvement at both ends of the pitch when he takes his side to the Tulloch Caledonian Stadium, following the 3-3 draw in the first game in Dingwall.
"We have to do a lot better than we did against Motherwell to get through the cup match," he said.
"If we defend like that and don't take the chances we had we will be out the cup.
"We had other opportunities to score, very good opportunities, you would have to say they were sitters.
"We are not putting them in the net and are conceding at the other end so it is a wee bit kamikaze and we have to get away from that.
"We have to do better in certain situations. We cannot be so naive because good teams will pick us off.
"And with Inverness coming off an extremely good result we are going to find it extremely difficult.
"So the players will have to get themselves sorted out and
get ready for Tuesday night because we need one big performance to get through to the next round of the Scottish Cup."
Defender Scott Boyd is glad of the quick opportunity to make amends for Saturday's result in Lanarkshire.
"We won't have to wait long for another game," he said.
"It's a chance for us to set things straight and get back on track.
"The boys are kicking themselves after losing what we thought was a point at least, so we look forward to Tuesday and the boys will be buzzing as it's a derby.
"We felt a bit hard-done by the last time but we will go into this game with confidence as we do in every game."