Hibs have won only one of their last 10 cinch Premiership matches, a run which played a part in the sacking of manager Jack Ross last week.
However, former Hibs captain McPake is mindful of the fact Ross County were on a run of 10 games without a victory before they arrived at Dens Park and thrashed Dundee 5-0 in October.
He expects the Edinburgh side to be a dangerous opponent as they try to pick up a confidence-boosting result ahead of their Premier Sports Cup final showdown with Celtic on Sunday.
McPake said: "We'd be foolish to look at their bad run because look at the run Ross County were on when they came down here and beat us.
"Hibs are a very good team. They're on a bit of a poor run and they've lost their manager but they're in a national cup final on Sunday. I don't think they'll be looking ahead to that. They'll be fully focused on their game with us because they need points just as much as we do.
"Hibs are a massive football club and every time they play at home, their fans expect them to win. We know they're a good side with good players. For me, they're just on a bad run. It's as simple as that."
McPake, who played for Hibs in the 2012 Scottish Cup final against Hearts, does not expect the upcoming trip to Hampden to be a major distraction for Tuesday's opponents, who are still under the interim management of David Gray.
He said: "The only difference Hibs have got this midweek is if they get a red card for violent conduct against us, come the weekend someone misses a cup final. I've been in that position at Hibs and played in a match the week before a Scottish Cup final and that's the only thing in the back of your mind.
"Other than that, it's just another league game for Hibs. The demands at Hibs are to win every game, and their players know that. We've done our homework on Hibs.
"We saw that there was some changes to their style of play at the weekend (against St Mirren) but our full focus is on what we can do. If we go down there and get it right, we believe we can come back with all three points."
Dundee are without injured captain Charlie Adam as they bid to bounce back following Saturday's 3-2 defeat at Ross County, in which they led twice.
McPake said: "We've got plenty here that can hurt teams but we've just got to get it right at the other end consistently. We gave up three goals at the weekend that we shouldn't have but there were a lot of positives to take from the game.
"Saturday is forgotten about though. We need to go to Easter Road now and put on a performance if we want to come away with anything."