It left Celtic 10 points behind their arch-rivals with just 15 matches to play.
Even if they were to win the last two Old Firm derbies of the season, they would still need Rangers to slip up badly to complete a sensational comeback in the title race.
But Mowbray has refused to throw in the towel, a sentiment echoed by summer signing Fortune, who said: "Now we have to win every game that is coming.
"It will be difficult but we can do it. Why not?
"We've shown that we are a big team, play very well and have a lot of chances.
"We have to complete that with goals and not conceding.
"We will do it, I'm confident about that."
Tuesday night's defeat, the 11th in 36 games since Mowbray took charge, came less than 24 hours after Celtic's title hopes appeared to be reignited by the signing of Robbie Keane.
The on-loan Tottenham striker had a debut to forget at Rugby Park but Fortune backed the man who has cost a combined £70million in his career to come good.
"Robbie's a top player and he showed it," the French forward added.
"We are very happy that he's signed for Celtic.
"He will bring something more for the team and he's a good signing."
Keane was one of two debutants in yesterday's starting XI, which featured just five players who were at the club last season.
"It's not a problem," said Fortune of the huge turnover of staff under Mowbray.
"We need time but, as I say, it's only top players in the team.
"We know what we have to do, so we will do it."
The 28-year-old, who saw a header cleared off the line last night, added: "To win the title you need a lot of character.
"We have to show that we want to win."
Mowbray's misery was compounded by injuries to Andreas Hinkel and Jos Hooiveld and a booking for Aiden McGeady that sees him suspended for the February 20 clash with Dundee United.