Rangers failed to get their Irn-Bru Third Division campaign off to a winning start last weekend when they were held 2-2 at Peterhead.
It was a result and performance which brought criticism from manager Ally McCoist, and now summer signing Black wants to ensure his side make amends with a performance at Ibrox.
He said: "We are all looking forward to the game.
"We know there are going to be tough games in the Third Division this season and maybe last weekend was a wee bit of an eye-opener for some of the lads.
"It's going to be a case of rolling up the sleeves and doing the hard bit first.
"We have another league game tomorrow and we will go into it with the right attitude this time."
Black, who was jeered as he made his Scotland debut on Wednesday, has enjoyed the opening weeks of his new life at Rangers and he remains as excited about the future as he was when he checked in at Ibrox for the first time at the start of the season.
He said: "It's been brilliant. The set-up at Rangers is unbelievable. The facilities at the training ground are excellent, the dressing room is great and I've enjoyed coming into work every day.
"I need to say the fans have also been fantastic with me. They've really got behind me and all the players."
Meanwhile, the Association of Tartan Army Clubs has condemned those Scotland fans who booed Black.
Speaking for ATAC, Jim Brown said: "Given this was Ian's full international debut, an occasion he has described as being the pinnacle of his career to date, these actions are disappointing."