Out of the Champions League, Europa League, Co-operative Insurance Cup and 10 points adrift of Rangers in the SPL, Celtic arguably cannot afford to slip up at East End Park.
Although Mowbray acknowledged some fans will be worried by the club's results since he took charge in the summer, he insisted any doom-mongering is limited almost exclusively to the media.
"You're reading your own media, if that makes sense," he said.
"My philosophy doesn't change. I bring a philosophy of what will bring long-term success and continue down that road.
"When it's done, the evidence is there; it'll be in your face."
He added: "I don't see the panic, to be fair. I don't see the panic, I don't hear the panic, it doesn't interest me.
"I get on with my job, build a team that will give us long-term success."
When challenged that supporters were genuinely concerned about how the team have performed this season, Mowbray said: "I've got every respect for our fans; they're up there with the best in the world.
"And yet the manager of the football team can't listen to every fan because we've got millions of them all over the world.
"There'll be some fans who are not very happy, some fans who want change.
"But there are a lot of fans who I bump into on the street who say, 'Keep the faith - it will come'.
"We get disappointed - hugely disappointed - when we don't win football matches.
"But there has to be a bigger picture of where we're taking this club and where we're going to be and the foundations that we put in place."
Mowbray refuted suggestions Sunday's game had taken on an extra significance as a result of Tuesday night's shock SPL defeat at Kilmarnock.
"No, I don't think so," he said.
"It's a game we have to go and win, as we try to win every game."
Pressed further, he snapped back: "What do you want me to say?
"We go and try to win the next football match - that's every week. The league game coming on Wednesday night; we've got to go and try to win that.
"Hopefully, another cup game will come; we've got to try to win that.
"We don't not try to win any football matches."
Despite repeating his recent pleas for patience, Mowbray said he was "hugely disappointed" to have fallen 10 points behind Rangers and admitted his grand plan was meant to bring success from the outset.
The Celtic boss also confirmed fit-again midfielder Scott Brown would captain the side for the rest of the season, despite acknowledging concerns over his suitability for the role.
"You're not going to change his personality overnight," Mowbray said of the man he also managed at Hibernian.
"He has the potential for flare-ups, because that's his personality.
"Since the day I walked into Hibs all those years ago, I could understand Scott's personality. He wants to win and he wants to be a winner out on the field, and he pushes himself really hard for that - and it's not a bad ingredient to have.
"Sometimes it needs tempering, of course. But you shouldn't be criticising him for the fire in his belly."
Mowbray did not consider loan star Robbie Keane for the role, even though he believes the Tottenham striker is just the kind of character the dressing room needed following the departure of a host of experienced players.
"He brings some personality," said Mowbray, who did not expand on how the club managed to finance his move.
"We've lost some personality over the last few months.
"Robbie's an experienced player; he brings a voice.
"He's a very good professional, works extremely hard in training, has got a great work ethic, does everything you ask of him and that's all I can ask."
Scottish Cup 2009/10 Win Outright: Celtic 6/4