Caley Thistle travel to Edinburgh on Saturday having taken just one point from four Clydesdale Bank Premier League games and exited both cup competitions in the past month.
Hearts knocked them out of the Scottish Communities League Cup on penalties and have drawn twice against Inverness this season.
But Butcher thoroughly enjoyed their previous trip to Gorgie when his men came back to claim a point despite having Richie Foran sent off.
And Caley Thistle dominated against Hearts at home before being denied three points by a last-minute penalty.
Butcher, who is still without knee-injury victim Foran, said: "Hearts on Saturday is a good one because, having lost the semi-final on penalties, that's still a bit raw.
"But we haven't beaten Hearts in the league. We feel Tynecastle is a good place. We went down there and at 2-0 down and managed to get a draw and played very well in the second half.
"We have nothing to fear and nothing to worry about and every reason to look forward to travelling down there and trying to get this win that would get us going again.
"We haven't won for a while and it's high time we got back to winning ways and we are not bothered how it comes."