Hughes replaced Terry Butcher at the start of December and signed a two-and-a-half year deal with the Highland club.
Amid a mixed start to his Caley career, he has yet to savour victory in front of his own support - losing to Aberdeen, Celtic and rivals Ross County - but is hoping his side can put that right in the Scottish Premiership game against the Taysiders.
He told Inverness' YouTube channel: "We have been working really hard this week, the players have been great in training and hopefully we can take that into the game and make sure that the three points are staying in Inverness.
"It would be nice to get that monkey off my back, with my first home win.
"But I can't ask any more of the boys in what they are giving me in effort and commitment and at times we have been playing good football.
"At times we have been possibly trying too hard and leaving ourselves open to counter attacks, resulting in giving ourselves too much to do to win the game.
"So hopefully we can correct that and get back to winning ways."
Hughes was boosted by the news this week that Carl Tremarco and Danny Williams have signed extended contracts at the club.
United manager Jackie McNamara will add on-loan Brentford striker Farid El Alagui to his squad.
Defender Gavin Gunning is fighting to shake off a leg knock in time to play.
McNamara believes his side can build on their last-gasp draw with Hibs.
The Tangerines fought back to earn a late point in last weekend's 2-2 draw with Hibs after looking down and out with time running out.
But they defied the odds to level through Brian Graham's last-minute equaliser and McNamara believes they can use that as a catalyst ahead of this weekend's trip north.
McNamara said: "It would be ideal if we could start as we finished against Hibs and take the game to them.
"We showed good battling qualities against Hibs and in any game you would like to get on the front foot.
"That's what we hope to do and try to do the things we know we're good at.
"We did well to get the game back against Hibs but it's never ideal when you have to chase things.
"We know this will be a tough game against Inverness but it's one we're relishing for all the right reasons.
"They will want to try and get the ball down to play like ourselves so we will have to take our chances when they come our way."