The Highlanders head into the second round tie at Gayfield on the back of a 4-2 reverse at the hands of the Scottish champions at the weekend.
Caley Thistle were trailing 4-0 before netting a couple of late consolation goals, but Butcher says the cup clash is simply about ensuring they are in the draw for the next round.
"For us, it's not a case of putting things right," he said
"It was a bad day at the office on Saturday and we've got next Sunday to make amends for that in terms of putting on a much better performance against Motherwell.
"Our thoughts are concerned with making progress in this cup and getting through this tie - it's as simple as that.
"We've got to do enough on the night to ensure we are in the hat for the next round. How we do that is immaterial in many respects.
"We had a good chat about the game on Saturday, which is now history, and we have immediately turned our thoughts to Arbroath."
Inverness lost to lower-league opposition in the competition last season, and Butcher still remembers the disappointment.
"Bearing in mind what happened last year at Ayr United, the players who were here certainly won't take anybody for granted or underestimate them," he added.
The Inverness boss would love to deliver the silverware this term after a disappointing run in the cups so far.
"Kilmarnock won it last year and it would be nice for us to win it.
"We've not had a real cup run since we've been here. We never seem to get further than the quarter-finals so it would be nice if we could do it," Butcher said.
Meanwhile, youngster Nick Ross will see a specialist on Wednesday to determine whether or not he needs surgery after suffering a dislocated shoulder at the weekend.
"He's in very good hands but it's disappointing for him," Butcher said.
"It's his first major injury in football. He came in and made his first start on Saturday and was looking good at that stage.
"We will see what the specialist says and go on his report and recommendation.
"If he does require an operation, he's in very good hands here. If not, his recuperation will be a lot quicker."