Despite closing to within two points of their opponents, John Hughes' men are refusing to talk about splitting the Old Firm.
But they are under orders to finish as the best of the rest, a position they briefly surrendered to Dundee United this month.
Centre-half Hogg insists failure to hold onto third place is not an option ahead of Saturday's game with St Mirren.
"That'll be the ultimate disappointment because we've managed to perform at a level where we've been sat second, third in the league for most of the season," he said.
"It'll be a major disappointment of the season if we do drop out.
"It's something I'm focused on, making sure it doesn't happen."
Hughes went public with his target for the season last weekend but Hogg revealed the squad knew all about it ever since the boyhood Hibs fan took charge last summer.
"We've had that goal all season to be honest," he said. "It's nice now that it's out in the open and we can go about our business knowing that's what we need to achieve."
And if it was down to ability, Hogg insists the Edinburgh club will have third place wrapped up come May.
"That's not in doubt," the 24-year-old said. "Ability-wise, we've got a number of players that could play for any team in the league.
"What has been scrutinised ever since I've been at the football club has been the mental attitude and sometimes the application of the team.
"It's been a lot better this year in patches and we need to really improve on that in the second part of the season."
It appears a two-horse race with United for third but Hogg insists there are contenders even as far down as seventh.
"If we don't win for two or three games, we're down to fifth - that's the way this league works," he said. "You can't rule anyone out.
"There could be a team even below Aberdeen who will push right up.
"We need to go on a consistent run of games, like we did in the first half of the season.
"That'll make sure we're up there fighting come six, seven games to go."
Hogg could have regular partner Sol Bamba back alongside him tomorrow after the Ivory Coast defender returned from African Nations Cup duty.
"He's a player who's just played in a major international tournament," Hogg said. "We can do with every good player that we've got.
"The gaffer will assess him physically and mentally and see where he's at.
"If he's back in the team, he's back in the team."
Paul Hanlon has filled in for Bamba of late and Hogg praised the youngster's contribution, saying: "I get on really well with Paul.
"He's got a great temperament and has done ever since I came to the football club.
"He's got a lot of potential; he's the type of lad who will work hard and get on with things.
"It's been nice to see him going well in the last couple of weeks.
"He's still a young guy and it's up to me to help him through games."