Micky Mellon's side went into the game against the Staggies at Tannadice on a high following a 3-0 cup quarter-final win at Aberdeen the previous week.
But County, fighting for their Premiership survival, took three deserved points back to Dingwall as they climbed out of the bottom two in the table.
First-half goals from striker Jordan White and defender Alex Iacovitti moved the Highland club one point above Kilmarnock and three ahead of bottom side Hamilton, whom they host on Wednesday week.
Midfielder Butcher turned his attention to Hibernian at Hampden next Saturday as United look to get to the final against either St Mirren or St Johnstone.
The 30-year-old told DUTV: "The result and performance was obviously disappointing.
"We spoke at length in the dressing room and it is something that needs to be put to bed.
"Off the back of a really good performance last week we didn't expect that but sometimes it is a good thing. You try to find the positives in it and we know now there is a massive reaction needed.
"You want to go into these games with confidence but sometimes these performances give you little bit of fire that you need again.
"Being as poor as we were, we can go into that game with the fire in our belly knowing how massive that game is for the club and for ourselves and really come out the traps like we did last week.
"These performances happen. We have been really consistent up until now, that's why we are safe.
"Like I said, we need to put it to bed and we go into the game with fire in our belly.
"It is a massive week for us and our preparation will be spot on.
"We pick ourselves up and go again next week. We know what is at stake."
Mellon believes his players will have shrugged off the disappointment for the game against Hibs.
He said: "That is an easy one. It is a semi-final of a cup.
"If you don't get up for games like that at the national stadium then we do have problems.
"What I will be trying to do is make sure they have a composed mentality rather than being too high. I wouldn't worry about it being too low.
"So get them composed in their thinking, get them back on their jobs again and get us facing in the right direction for a massive game on Saturday."
County boss John Hughes was delighted with his side's performance and the clean sheet.
He said: "We were solid. It helps to get our goals. We didn't have to go chasing it in the second half and it was about keeping our shape and being professional.
"Goals put us in a better place but you've got to go and get them against a United team that were very, very good when I saw them last week."