Hearts have so far sold about 10,000 tickets for Saturday's Easter Road clash while Caley Thistle are unlikely to sell many more than 2,000.
But Inverness are used to defying the odds against bigger teams this season, sitting second in the Clydesdale Bank Premier League.
And Butcher, assistant Maurice Malpas and captain Richie Foran all helped Motherwell beat Hearts at the same stage and venue seven years ago, so playing Hearts miles from their home ground holds no fears.
"Hearts will outnumber us, not doubt about that, maybe even five, six, seven to one.
"But we always do well away from home. We always carry a good support away from home, very noisy. It's not the biggest but they ain't half noisy.
"We will maybe have 10 times more away fans than we normally do. So from our point of view it's brilliant and I'm sure they will make a helluva lot of noise and cheer us on."
Butcher was delighted with the response of fans when his team beat Aberdeen 3-0 on Saturday to continue their excellent season.
"If I've done nothing in my career at Caley Thistle, I've got the main stand to sing at games. I don't think any Caley Thistle manager has done that.
"Last week, orchestrating the main stand, I have never done that before. We have some great supporters and I'm sure they will come down in their numbers. But most important they have got to bring their singing voices and cheer us all the way to Hampden."