Caley Thistle lost their unbeaten record at Aberdeen, although they stayed top of the Scottish Premiership.
Dundee fell to defeat at Falkirk as their indifferent start to the Scottish Championship season continued - they sit in fourth place with eight points from six games, half the total of leaders Hamilton.
But Butcher knows former Rangers team-mate John Brown will have his players fired up for the third-round encounter.
Butcher said: "We have to respect Dundee. The last time at Dens we drew 1-1, but the previous time we won 4-1 so the boys have got good memories of the place.
"They will be hard-working, they will fight very hard. They have players with good experience and players who can hurt you. If you allow them to play, they can play pretty well.
"They have had a mixed bag of results in the Championship, a side still blending together. Like ourselves, they lost on Saturday, at Falkirk, so both managers will be expecting their teams to bounce back."