Ferguson was appointed on Monday after Philippe Clement's sacking by the Glasgow club 24 hours earlier.
The former Rangers captain has previously been in charge of Clyde, Kelty Hearts and Alloa.
Since his disappointing spell with Alloa ended in February 2022, Ferguson has combined media work with an ambassadorial role at Ibrox.
Fans have been critical of the decision to entrust the 47-year-old with the job despite his lack of managerial experience at the highest level.
But Ferguson is adamant he deserves the chance to prove his worth, starting with Wednesday's league game at Kilmarnock.
"Judge me at the end of the three months," the former Scotland midfielder said at his first press conference on Tuesday.
"I have no issue with that. Everybody's entitled to their opinion. I would rather be judged come the end of the season, but also know I'm going to be judged game by game.
"This is just the nature of the beast when you're at Glasgow Rangers."
Ferguson's managerial career lasted almost eight years but he had started to come to terms with the possibility he would never get another chance, until his phone rang with the job offer following Clement's exit.
"I had a quiet life for a few years," said Ferguson, who has brought in former Gers team-mates Neil McCann, Billy Dodds and Allan McGregor to join his coaching staff.
"I was enjoying a new role at the club. I was a club ambassador for the past year-and-a-half.
"But listen, when you get offered the opportunity, there was no way I was turning it down. I'm just glad I took it and we'll see where it goes.
"But look, I'm confident. I'm confident in my ability, I'm confident in my staff's ability and also the players. I wouldn't be sitting here if I didn't feel ready.
"Did I want to go back into coaching and management? If I'm brutally honest, I wasn't thinking about it. But when that phone call comes, there was no way that I was going to turn it down."
With Rangers 13 points adrift of Scottish Premiership leaders Celtic and reeling after consecutive home defeats by Queen's Park and St Mirren, Ferguson has laid down the law to his players.
"I expect them to win games of football," he said. "I expect them to give me everything they've got, because that's one thing I'll give them and my coaching staff as well.
"I had a brief meeting with them for five or 10 minutes and I got it across and they fully understand my expectations."